Question about spinor wavefunction

In summary, the conversation is about representing the state of an electron in a hydrogen atom in the position representation as a spinor wavefunction. The question asks for help in calculating the sum using Dirac wave functions, or if the hydrogen atom problem needs to be solved first. The difference between the state and the spinor wavefunction is clarified and an example is requested. The exercise is from the book Principles of Quantum Mechanics by Hans C. Ohanian. The conversation ends with a request for the three spinor wave functions and an explanation of what is not understood.
  • #1
Orion_PKFD
9
0
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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  • #2
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?
 
  • #3
That is only a part of the state in the position representation, not the spinor wavefunction.
 
  • #4
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?
 
  • #5
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.
 
  • #6
I do not see your problem.

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

1. What is a spinor wavefunction?

A spinor wavefunction is a mathematical function that describes the quantum mechanical properties of a spinor particle, which is a type of fundamental particle that has a half-integer spin value. It is used to calculate the probability of finding the particle in a particular state or location.

2. How is a spinor wavefunction different from a regular wavefunction?

A spinor wavefunction is different from a regular wavefunction in that it takes into account the spin of the particle, which is a quantum mechanical property that determines how the particle will behave in a magnetic field. A regular wavefunction does not include this information.

3. What is the significance of the spinor wavefunction in quantum mechanics?

The spinor wavefunction is significant in quantum mechanics because it allows us to describe and understand the behavior of spinor particles, which are fundamental building blocks of matter. It is also used in many important calculations and theories in quantum mechanics.

4. How is the spinor wavefunction related to the Pauli exclusion principle?

The spinor wavefunction is related to the Pauli exclusion principle because it describes the spin state of a particle, which is one of the factors that determines whether or not two particles can occupy the same quantum state. The Pauli exclusion principle states that no two particles with the same quantum numbers can occupy the same state, and the spinor wavefunction helps us calculate and understand this behavior.

5. Can the spinor wavefunction be observed or measured?

No, the spinor wavefunction itself cannot be directly observed or measured. It is a mathematical construct that helps us understand the behavior of quantum particles. However, the effects of the spinor wavefunction can be observed through experiments and measurements of particles with spin, such as electrons or protons.

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