| Topic: |
Science > Physics |
| User: |
"SkanderH" |
| Date: |
26 Jan 2005 04:29:43 AM |
| Object: |
About superpositions and orbitals |
An important result in QM is the principal of superposition of states,
e.g that a system can be in a linear combination of basis states at
the same time, until measured, when the system collapses to one of
these basis states. Another important result of QM is the model of
the hydrogen atom with orbitals and quantum numbers replacing Bhor's
planetary model and older classical ideas. Now my question is:
In the QM model of the hydrogen model what are the basis states and
what is the superposition:
- Is one orbital the superpostion and the basis states the different
positions of the electron around the orbital? or
- Does each orbital represent a basis state and the electron is
actually in all orbitals, and collapses to one orbital when we fire a
photon at it or something?
Thanks
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Posted at:
www.GroupSrv.com
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| User: "Franz Heymann" |
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| Title: Re: About superpositions and orbitals |
26 Jan 2005 08:00:21 AM |
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"SkanderH" <skander@hrt.dis.titech.ac-dot-jp.no-spam.invalid> wrote in
message news:41f77117$1_1@Usenet.com...
An important result in QM is the principal of superposition of
states,
e.g that a system can be in a linear combination of basis states at
the same time, until measured, when the system collapses to one of
these basis states. Another important result of QM is the model of
the hydrogen atom with orbitals and quantum numbers replacing Bhor's
planetary model and older classical ideas. Now my question is:
In the QM model of the hydrogen model what are the basis states and
what is the superposition:
- Is one orbital the superpostion and the basis states the different
positions of the electron around the orbital?
Each orbital of the Hydrogen atom is in fact a "basis state" of the
solution of Schrodinger's equation for the problem of the Hydrogen
atom.
- Does each orbital represent a basis state
Yes
and the electron is
actually in all orbitals, and collapses to one orbital when we fire
a
photon at it or something?
No. Normally it is in the ground state.
Franz
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| User: "SkanderH" |
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| Title: re:About superpositions and orbitals |
27 Jan 2005 03:29:12 AM |
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Generally, the energy eigenstates are used (i.e. the states
which have definite energies), because these are the
stationary states. Most often one chooses the basis states
also to be eigenstates of angular momentum.
Yes, the orbitals are commonly chosen as the basis states.
[quote:61353470f2]Each orbital of the Hydrogen atom is in fact a
"basis state" of the
solution of Schrodinger's equation for the problem of the Hydrogen
atom.
[/quote:61353470f2]
But,
No. Normally it is in the ground state.[quote:61353470f2]and the
electron is actually in all orbitals,
Huh? No. It is in exactly one.
[/quote:61353470f2]
If the electron is in only one orbital at a time, why is the orbital
un eigen or basis state (I hope I am not confusing two things)? Why
can't there be a superposition of several orbitals?
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| User: "Franz Heymann" |
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| Title: Re: re:About superpositions and orbitals |
27 Jan 2005 02:46:32 PM |
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"SkanderH" <skander@hrt.dis.titech.ac-dot-jp.no-spam.invalid> wrote in
message news:41f8b468$1_2@Usenet.com...
Generally, the energy eigenstates are used (i.e. the states
which have definite energies), because these are the
stationary states. Most often one chooses the basis states
also to be eigenstates of angular momentum.
Yes, the orbitals are commonly chosen as the basis states.
[quote:61353470f2]Each orbital of the Hydrogen atom is in fact a
"basis state" of the
solution of Schrodinger's equation for the problem of the Hydrogen
atom.
[/quote:61353470f2]
But,
No. Normally it is in the ground state.[quote:61353470f2]and the
electron is actually in all orbitals,
Huh? No. It is in exactly one.
[/quote:61353470f2]
If the electron is in only one orbital at a time, why is the orbital
un eigen or basis state (I hope I am not confusing two things)? Why
can't there be a superposition of several orbitals?
Because the basis states are an orthogonal set. If the state is
described by one of them, it cannot be expanded in terms of a
superposition of the other eigenstates..
Franz
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| User: "Bjoern Feuerbacher" |
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| Title: Re: About superpositions and orbitals |
27 Jan 2005 05:25:43 AM |
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Your attributions were mangled. I corrected them.
SkanderH wrote:
Generally, the energy eigenstates are used (i.e. the states
which have definite energies), because these are the
stationary states. Most often one chooses the basis states
also to be eigenstates of angular momentum.
Yes, the orbitals are commonly chosen as the basis states.
[quote:61353470f2]Each orbital of the Hydrogen atom is in fact a
"basis state" of the
solution of Schrodinger's equation for the problem of the Hydrogen
atom.
[/quote:61353470f2]
But,
No. Normally it is in the ground state.[quote:61353470f2]and the
electron is actually in all orbitals,
Huh? No. It is in exactly one.
[/quote:61353470f2]
If the electron is in only one orbital at a time, why is the orbital
un eigen or basis state (I hope I am not confusing two things)?
Err, why on earth couldn't the orbital be an eigenstate of
energy if the electron is in only one orbital at a time?????
Why can't there be a superposition of several orbitals?
If all these orbitals have the same energy, this can
indeed happen. But then you only have a new set of orbitals,
and the electron is still in only one "hybrid orbital".
Bye,
Bjoern
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| User: "Bjoern Feuerbacher" |
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| Title: Re: About superpositions and orbitals |
26 Jan 2005 07:42:36 AM |
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SkanderH wrote:
An important result in QM is the principal of superposition of states,
e.g that a system can be in a linear combination of basis states at
the same time, until measured, when the system collapses to one of
these basis states. Another important result of QM is the model of
the hydrogen atom with orbitals and quantum numbers replacing Bhor's
planetary model and older classical ideas. Now my question is:
In the QM model of the hydrogen model what are the basis states
Generally, the energy eigenstates are used (i.e. the states
which have definite energies), because these are the
stationary states. Most often one chooses the basis states
also to be eigenstates of angular momentum.
and what is the superposition:
- Is one orbital the superpostion and the basis states the different
positions of the electron around the orbital? or
If you take the position eigenstates of the electron as your
basis states, the orbitals are indeed superpositions. But
that's not how it is generally done.
- Does each orbital represent a basis state
Yes, the orbitals are commonly chosen as the basis states.
and the electron is actually in all orbitals,
Huh? No. It is in exactly one.
and collapses to one orbital when we fire a
photon at it or something?
Huh? Do you mean when we measure its position? Then the
electron collapses *from* an orbital (an energy eigenstate,
commonly used as basis states) *to* a position eigenstate.
Bye,
Bjoern
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