| Topic: |
Science > Physics |
| User: |
"Warrick FitzGerald" |
| Date: |
06 Apr 2005 12:24:07 PM |
| Object: |
Quantum Physics for mere humans |
Hi All,
I’m currently in the process of learning the basics of Quantum Physics.
I’m having some problems getting started, as I feel like every time I
follow a specific direction it just leads me to a labyrinth of new
information.
Can someone please suggest a structured approach to getting started in
the field? Books \ Course \ Online ..
I’m also not a very strong math person …aka I have not done calculus at
all. I’m certain those that use math in the field would consider this an
essential skill, so I guess my question really boils down to:
1. How do I get a good grounding in Quantum Physics?
2. Is it completely necessary to have strong math skill to get
anywhere in this form of study?
Thanks
Warrick
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| User: "David Macmanus" |
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| Title: Re: Quantum Physics for mere humans |
11 Apr 2005 06:37:35 AM |
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"Warrick FitzGerald" <subs.nntp.wfitzgerald@crtman.com> wrote in message
news:XWU4e.33$cv3.568@news.uswest.net
I’m currently in the process of learning the basics of Quantum Physics.
I’m having some problems getting started, as I feel like every time I
follow a specific direction it just leads me to a labyrinth of new
information.
Yep, that's not surprising
Can someone please suggest a structured approach to getting started in
the field? Books \ Course \ Online ..
I’m also not a very strong math person …aka I have not done calculus at
all. I’m certain those that use math in the field would consider this an
essential skill, so I guess my question really boils down to:
1. How do I get a good grounding in Quantum Physics?
2. Is it completely necessary to have strong math skill to get
anywhere in this form of study?
Here's a question for you. How much do you really want this? How much
hard grind are you willing to put in? Are you expecting to achieve what
you want after a couple of months? How deep do you want to go? Do you
want to understand the mathematics or not?
I don't need to tell you that QM is a pretty difficult thing to
underdstand. If you want to understand what people mean when they talk
about the 'weirdness' of QM (like the double slit experiment) then you
can do that in an evening. But if you want to understand how to solve
the Schroedinger equation and a lot more besides then you are in for a
long haul. There's a lot mathematics involved. One approach would be to
get a fairly basic QM book, eg. the recent one by Phillips, and read
until you get stuck on the maths. Then stop and set yourself the task of
getting the necessary background to understand that maths. This way you
pick up the maths as you go along and don't have to spend two years
learning maths in the hope that it will be useful to you when you
eventually get around to picking up a physics book.....
Until I know exactly what you want to achieve then it's difficult to
advise,except to say that if you want any kind of a decent understanding
you will need to understand the maths and it will take you long time to
really get anywhere.
Sorry to be the bearer of bad news........
Good luck whatever,
David.
PS. My guess is that 99% of people who set out with the notion that they
will be able to self-teach themselves QM fail.
--
Posted via Mailgate.ORG Server - http://www.Mailgate.ORG
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| User: "Gregory L. Hansen" |
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| Title: Re: Quantum Physics for mere humans |
06 Apr 2005 12:54:10 PM |
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In article <XWU4e.33$cv3.568@news.uswest.net>,
Warrick FitzGerald <subs.nntp.wfitzgerald@crtman.com> wrote:
Hi All,
I’m currently in the process of learning the basics of Quantum Physics.
I’m having some problems getting started, as I feel like every time I
follow a specific direction it just leads me to a labyrinth of new
information.
Can someone please suggest a structured approach to getting started in
the field? Books \ Course \ Online ..
I’m also not a very strong math person …aka I have not done calculus at
all. I’m certain those that use math in the field would consider this an
essential skill, so I guess my question really boils down to:
1. How do I get a good grounding in Quantum Physics?
2. Is it completely necessary to have strong math skill to get
anywhere in this form of study?
Thanks
Warrick
--
"Is that plutonium on your gums?"
"Shut up and kiss me!"
-- Marge and Homer Simpson
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| User: "Uncle Al" |
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| Title: Re: Quantum Physics for mere humans |
06 Apr 2005 02:11:42 PM |
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Warrick FitzGerald wrote:
Hi All,
I’m currently in the process of learning the basics of Quantum Physics.
I’m having some problems getting started, as I feel like every time I
follow a specific direction it just leads me to a labyrinth of new
information.
There is no understanding QM. All you can hope for is to be facile
with the deep maths that accurately predict observations. The shallow
presentations default to wrote memorization. That sums to a very
small toolbox.
Can someone please suggest a structured approach to getting started in
the field? Books \ Course \ Online ..
I’m also not a very strong math person …aka I have not done calculus at
all. I’m certain those that use math in the field would consider this an
essential skill, so I guess my question really boils down to:
1. How do I get a good grounding in Quantum Physics?
2. Is it completely necessary to have strong math skill to get
anywhere in this form of study?
QM is nothing but its maths - and even they are not rigorously tied to
it. QM is assembled not derived. Euler's equation ties algebra to
analytic geometry. If you do one you are also doing the other.
Noether's theorem ties physical properties to mathematical
symmetries. Faced with a big mixed property menu look at the small
isolated symmetry menu. NOTHING simplifies quantum mechanics. The
best you can hope for is to be complicated in a more usable way. Like
epicycles vs. a heliocentric solar system, QM is probably an awful
model begging for a stroke of insight.
Description Geometry Dynamics
of state
---------------------------------------------------------
Newtonian Mechanics | Vector in | Euclidean | Newton's
| phase space | 3 + time | laws
----------------------------------------------------------
Special Relativity | Vector in | Minkowski | Newton's
| phase space | 4 dimen | laws
----------------------------------------------------------
General Relativity | Vector in | pseudo- | Newton's
| phase space | Riemannian| laws
----------------------------------------------------------
Quantum Mechanics | Vector in | Euclidean | Newton's
| Hilbert space | 3 + time | laws
----------------------------------------------------------
Relativistic QM | Vector in | Minkowski | Newton's
| Hilbert Space | 4 dim | laws
----------------------------------------------------------
QM of black holes | Vector in | pseudo- | Newton's
| Hilbert Space | Riemannian| laws
----------------------------------------------------------
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "" |
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| Title: Re: Quantum Physics for mere humans |
15 Apr 2005 05:29:26 PM |
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Uncle Al wrote:
There is no understanding QM. [...]
QM is nothing but its maths
QM is probably an awful
model begging for a stroke of insight.
(Chart showing the formalism for states, geometries and dynamics
deleted).
Actually, classical states can also be described in a Hilbert space.
It's just that the representation is reducible at the extreme: one
superselection sector for each classical mode.
In fact that's the essential bridge between the two: the center of the
algebra of observables is spanned by the superselection observables.
In the most general situation (QM with superselection) you therefore
have a composite of quantum degrees of freedom + classical degrees (the
superselection modes). The only drawback (as shown by Neumaier (sp?)
who's posted occasionally here and in s.p.r.) is that information can't
be transmitted from the quantum sector to the classical sector since
the latter is preserved by all automorphic dynamics ("automorphic" is
the generic term for any evolution that transforms the algebra of
observables by automorphism). That leads inevitably to the notion of
irreversibility and of the dynamic semigroup.
[One way to implement that idea is to simply back away from the
hypothesis of there being a universal pure state in the first place,
and treat the manifold as comprising compact regions, each having a
causal boundary. Doing the partial trace over the causal boundary
gives you a thermal (mixed) state. Information that passes through the
boundary effects a form of irreversible dynamics. Effectively the
outside of the region is classical and information that passes out of
the region is passing into the classical modes. This is a form of
"coarse-graining" (through the use of the term in this context is
ironic) which complements the coarse-graining that lies at root in
decoherence.]
Likewise, the quantum degrees of freedom, as you're almost certainly
aware of, can be represented in a phase space by distributions which
may go negative.
The natural interpretation is that the negativity provides a natural
constraint on which subspaces are "allowable" (e.g. a box enclosing one
phase space mode of area less than Planck's constant would be
forbidden).
This is made precise by the Berezin quantization prescription which
directly represents the phase space points of the classical theory in
the corresponding quantum state space as "coherent" states. Varney
made a point about those, if you'll recall, in s.p.r. a year or two ago
when I pointed out that no pure classical states exist. They represent
the closest analogue within QM to classical pure states (i.e. to phase
space points).
[To use an extreme example: you can actually write down coherent states
for a spin 1/2 system. In effect, each state is represented by a
2-valued function combinations of exp(+/- phi/2). The "reproducing
kernel" squashes down general function to combinations of these.
Single-valuedness is recovered within the expectation value, since this
involves quadratic combinations of the functions representing the
states.]
The forbidden region idea is implemented through the relation of
Berezin quantization to the Wigner phase space prescription. Operators
described within the Berezin formulation are related to the
corresponding Wigner space operators via a Gaussian smearing that
effects a convolution with a Gaussian of area equal to the Planck's
constant per classical mode.
As you can see by these two points, the distance between (and
difference between) classical and quantum theory is a lot less than is
otherwise held to; likewise for the modes of interpretation.
Each point of one has a closely analogous point in the other, and vice
versa. That's to be expected since the two theories are so close to
being empirically identical that their difference wasn't even visible
until around the middle part of the 19th century; and wasn't recognized
as such until the end of the 19th century. Therefore, their
mathematical formulations can likewise be rendered in nearly congruent
fashion.
The classical/quantum treatment of the Kepler problem is an
illustration of this ("Orbitals as Orbits...").
I made a point about the issue in the Prologue to the treatise I'm
working on, the relevant quote reproduced below:
One of the primary tasks of the treatise, therefore, is not just to
dispel the myth that quantum and classical physics are so radically
different as to actually require radically different formalisms (as
opposed to, say, of radically different formalisms being merely the
effects of different tastes and styles differentially applied to one
branch of physics vs. the other) but that their differences are in fact
far smaller and of far less physical content than is normally regarded,
and that they can be secured on a common foundation that in large
measure applies equally to both.
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| User: "Schoenfeld" |
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| Title: Re: Quantum Physics for mere humans |
07 Apr 2005 04:00:25 PM |
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Uncle Al wrote:
[remove]
QM is nothing but its maths - and even they are not rigorously tied
to
it. QM is assembled not derived. NOTHING simplifies quantum
mechanics. The
best you can hope for is to be complicated in a more usable way.
Like
epicycles vs. a heliocentric solar system, QM is probably an awful
model begging for a stroke of insight.
Looks like that 1 full standard deviation didn't accomplish much.
Welcome to your betters.
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| User: "PD" |
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| Title: Re: Quantum Physics for mere humans |
06 Apr 2005 03:25:13 PM |
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Warrick FitzGerald wrote:
Hi All,
I'm currently in the process of learning the basics of Quantum
Physics.
I'm having some problems getting started, as I feel like every time
I
follow a specific direction it just leads me to a labyrinth of new
information.
Can someone please suggest a structured approach to getting started
in
the field? Books \ Course \ Online ..
I'm also not a very strong math person ...aka I have not done
calculus at
all. I'm certain those that use math in the field would consider
this an
essential skill, so I guess my question really boils down to:
1. How do I get a good grounding in Quantum Physics?
2. Is it completely necessary to have strong math skill to get
anywhere in this form of study?
Thanks
Warrick
If you want a start, I suggest a book called "The End of Physics". It
won't teach you much about how to *do* quantum mechanics, but it will
give you an idea of what is conceptually demanding about it. There are
a number of other popular science books about quantum mechanics, as
well, all which talk about "quantum weirdness" or "quantum spookiness"
and all that.
If you want to know how to *do* quantum mechanics, though, you'll need
- calculus
- ordinary differential equations
- linear algebra (matrices)
- partial differential equations
at the very least
- complex variables
- group theory
after that.
Sorry, but I don't think there's a workaround.
PD
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| User: "" |
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| Title: Re: Quantum Physics for mere humans |
08 Apr 2005 03:34:38 PM |
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Warrick FitzGerald wrote:
Hi All,
I'm currently in the process of learning the basics of Quantum
Physics.
I'm having some problems getting started, as I feel like every time
I
follow a specific direction it just leads me to a labyrinth of new
information.
Click on the Internet Research FAQ under:
http://www.federation.g3z.com/Federation.htm
Reproduced in association with the Spire Project. More information on
mining information can be found from the links within the FAQ, which
includes links to the Spire home site. In time I will be adding
information under the Physics section. Sorry for the ads.
.
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| User: "GR_GR" |
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| Title: Re: Quantum Physics for mere humans |
06 Apr 2005 12:42:23 PM |
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Warrick FitzGerald wrote:
Hi All,
I’m currently in the process of learning the basics of Quantum Physics.
I’m having some problems getting started, as I feel like every time I
follow a specific direction it just leads me to a labyrinth of new
information.
Can someone please suggest a structured approach to getting started in
the field? Books \ Course \ Online ..
Start with a basic undergraduate modern physics textbook like:
Modern Physics for Scientists and Engineers, 2/E
http://vig.prenhall.com:8081/catalog/academic/product/0,4096,013805715X-SS,00.html
After you have gone through this, get Griffith's Intro to QM and the
Schaums outline related to QM.
Better yet, sign up at a university for a QM course.
I’m also not a very strong math person …aka I have not done calculus at
all.
Oh.
Ok.... first I would recommend you get book on calculus. Thomas and
Finny 11th is the latest I believe:
http://wps.aw.com/aw_thomas_calculus_11
And perhaps a Schaums outline for problems, and start chugging through it.
Better yet, sigh up at a cheap community college and take a calculus course.
Then, after you take calculus, take a basic calculus based physics course.
Then take a ugrad mechanics course, then start where I said with the
modern physics text.
I’m certain those that use math in the field would consider this an
essential skill, so I guess my question really boils down to:
1. How do I get a good grounding in Quantum Physics?
See above.
2. Is it completely necessary to have strong math skill to get
anywhere in this form of study?
Anywhere useful, that is not simply popularized pap.
If you are looking for inspiration to keep you going in your studies,
read Gribbin's In Search of Schroedinger's Cat.
Otherwise, start with the math then go for the QM.
You cannot run before you crawl.
Thanks
Warrick
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| User: "Rene Tschaggelar" |
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| Title: Re: Quantum Physics for mere humans |
06 Apr 2005 02:49:32 PM |
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Warrick FitzGerald wrote:
Hi All,
=20
I=92m currently in the process of learning the basics of Quantum Physic=
s.=20
I=92m having some problems getting started, as I feel like every time I=
=20
follow a specific direction it just leads me to a labyrinth of new=20
information.
=20
Can someone please suggest a structured approach to getting started in =
the field? Books \ Course \ Online ..
=20
I=92m also not a very strong math person =85aka I have not done calculu=
s at=20
all. I=92m certain those that use math in the field would consider this=
an=20
essential skill, so I guess my question really boils down to:
=20
1. How do I get a good grounding in Quantum Physics?
2. Is it completely necessary to have strong math skill to get
anywhere in this form of study?
Contrary to what others tell, QM is a bunch of concepts and
the rest is math.
You start with a hamiltonian, a differential equation that
links energy and time, as well as location and impulse.
It consists of the potential energy plus the dynamic energy.
With a lot of math you diagonalize it and get the behaviour
of the system.
Contrary to what others tell, a lot can be visualized once
you get familiar with it. Such that when the potential wall
is not infinitely steep, there is a certain probability to
have the particle in the wall itself.
I found the way QM is taught extremely dry. A lot of math
explained in all details, but only applied on trivial examples
such as the harmonic oscillator. Ah, yes, plus the hydrogen
atom.
And the output of QM for the student ? There are bound states
with distinct energy levels and there are scattering states
with no restriction on the energies. While we were able to
calculate a lot, none of the real stuff was in reach.
Well, the size of the parameterset was larger than possibly
solveable in analytical form.
My hint : get the concepts and the results and forget
about the rest. Especially when math is not your strong side.
Well, if it was, you'd possible have studied physics already.
Rene
--=20
Ing.Buero R.Tschaggelar - http://www.ibrtses.com
& commercial newsgroups - http://www.talkto.net
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| User: "Warrick FitzGerald" |
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| Title: Re: Quantum Physics for mere humans |
06 Apr 2005 05:24:21 PM |
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solveable in analytical form.
My hint : get the concepts and the results and forget
about the rest. Especially when math is not your strong side.
Well, if it was, you'd possible have studied physics already.
Rene
Thanks, I really do appreciate everyone's time and input.
Here's an example of where I'm coming from - I'll often read an article
along these lines
http://www.scienceagogo.com/news/20050110221715data_trunc_sys.shtml
and not quite grasp what the potential of this investigation \ finding is.
Although I very much appreciate the deep math that underlies a lot of
this - history in many cases has shown that by simple tinkering and
experimentation much can be derived. I'm far more of a hands on type of
person, Quantum Physics fascinates me and I'd love to have a practical
understanding of how to conduct experiments that demonstrate the nature
of the topic.
The suggestion of reading "The End of Physics" sounds like a good start,
as it's probably important to know what differentiates QF from classic
physics.
Just like I can buy a soldering iron from a Circuit City and create an
electric circuit from a bunch of electrons that I can not see, I'd love
to be able to do the same to experience the effects of QF.
Thanks again for reading my ramblings :)
Warrick
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| User: "Gregory L. Hansen" |
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| Title: Re: Quantum Physics for mere humans |
06 Apr 2005 07:53:38 PM |
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In article <42543d56$0$1163$5402220f@news.sunrise.ch>,
Rene Tschaggelar <none@none.net> wrote:
Warrick FitzGerald wrote:
Hi All,
I’m currently in the process of learning the basics of Quantum Physics.
I’m having some problems getting started, as I feel like every time I
follow a specific direction it just leads me to a labyrinth of new
information.
Can someone please suggest a structured approach to getting started in
the field? Books \ Course \ Online ..
I’m also not a very strong math person …aka I have not done calculus at
all. I’m certain those that use math in the field would consider this an
essential skill, so I guess my question really boils down to:
1. How do I get a good grounding in Quantum Physics?
2. Is it completely necessary to have strong math skill to get
anywhere in this form of study?
Contrary to what others tell, QM is a bunch of concepts and
the rest is math.
I always feel a little disheartened when someone with little physics
background asks how to learn quantum mechanics. And this is why:
You start with a hamiltonian,
What the hell is a Hamiltonian? You need to learn classical mechanics,
first, and the freshman physics book is necessary but not sufficient.
a differential equation that
Yep, you need the math.
links energy and time, as well as location and impulse.
It consists of the potential energy plus the dynamic energy.
Concepts that would be learned in the freshman physics course.
With a lot of math you diagonalize it and get the behaviour
of the system.
How the hell do you diagonalize something? In addition to calculus and
differential equations, let's pile on the linear algebra. And in an
important sense, quantum mechanics is all about the linear algebra, so
you're going to be hurting if you don't know it. At least I was, until I
got myself up to speed.
It's not really like learning that F=ma. The very vocabulary of quantum
mechanics derives from post-freshman physics.
Contrary to what others tell, a lot can be visualized once
you get familiar with it. Such that when the potential wall
is not infinitely steep, there is a certain probability to
have the particle in the wall itself.
Quantum mechanics is just another wave mechanics, but with an unusual
interpretation of the wave. The bad news is that wave mechanics of any
kind isn't easy. The good news is that everyone can visualize water waves
and light waves and sound waves, and they can visualize a quantum
wavefunction in a similar way with the potential standing in for the index
of refraction or the acoustical impedence or whatever.
--
"Coincidences, in general, are great stumbling blocks in the way of that
class of thinkers who have been educated to know nothing of the theory of
probabilities." -- Edgar Allen Poe
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