Question about spinor wavefunction

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    Spinor Wavefunction
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Discussion Overview

The discussion revolves around the representation of a specific quantum state of an electron in a hydrogen atom as a spinor wavefunction. Participants explore how to express the given state in the position representation, addressing both the mathematical and conceptual aspects involved in this process.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant asks for help in expressing the state |phi> in the position representation as a spinor wavefunction.
  • Another suggests using Dirac wave functions and calculating the sum, questioning whether the hydrogen atom problem needs to be solved first.
  • A participant clarifies that the initial response only addresses part of the state in the position representation, not the full spinor wavefunction.
  • There is a request for clarification on the difference between the position representation and the spinor wavefunction, along with an inquiry about the participant's familiarity with hydrogen atom solutions.
  • One participant emphasizes that the exercise is about using the spinor representation, asserting that the known solutions are not the focus of the problem.
  • Another participant requests the posting of the three spinor wave functions and asks for clarification on the specific points of confusion.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the problem and the necessary steps to solve it. There is no consensus on the best approach to represent the state as a spinor wavefunction, and the discussion remains unresolved.

Contextual Notes

Participants have not fully defined the assumptions regarding the spinor representation or the specific forms of the wavefunctions involved. The discussion also lacks clarity on the mathematical steps required to transition from the given state to the desired representation.

Orion_PKFD
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The question is the following:
At one instant, the electron in a hydrogen atom is in the state:

|phi>=sqrt(2/7) |E_2,1,-1,+> + 1/sqrt(7) |E_1,0,0,-> - sqrt(2/7) |E_1,0,0,+>

Express the state |phi> in the position representation, as a spinor wavefunction


How am I supposed to do this?

Some help would be very appreciated!:shy:
 
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Get your script with the Dirac wave functions

[tex]\psi_{E_2,1,-1,+}(r) = <r|E_2, 1, -1, +>[/tex]

etc. and calculate the sum.

Or do you have to solve the hydrogen atom problem first?
 
That is only a part of the state in the position representation, not the spinor wavefunction.
 
what is the difference? can you give us an example what your problem really is? do you already know the solutions (wavefunctions) for the hydrogen atom?
 
The idea here is representing the state as a spinor wavefunction. The solutions are known and don't matter for the case, all you need to do is use the spinor representation.

The exercise is exactly the one I wrote above. From Principles of Quantum Mechanics by Hans C. Ohanian.
 
I do not see your problem.

Can you post the three spinor wave functions and explain what you do not understand?
 

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