Question about spinor wavefunction

[Orion_PKFD]

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:

 

[tom.stoer]

Get your script with the Dirac wave functions

$$\psi_{E_2,1,-1,+}(r) = <r|E_2, 1, -1, +>$$

etc. and calculate the sum.

Or do you have to solve the hydrogen atom problem first?

 

[Orion_PKFD]

That is only a part of the state in the position representation, not the spinor wavefunction.

 

[tom.stoer]

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?

 

[Orion_PKFD]

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.

 

[tom.stoer]

I do not see your problem.

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