1. The potential function for the 2D harmonic oscillator is: V(x,y)=(1/2)mw²(x²+y²), where x and y are the 2D cartesian coordinates.
(a) Please write down the Schrodinger equation in x and y, then solve it using the separation of variables to derive the energy spectrum. Does it make sense relative to the 1D and 3D versions ([2,61] and [4.189])?
(b) Please find the degeneracy d(n) as a function of n for each energy En.

2. Spin. Please work on problem 4.49, but instead of the provided spinor X=A(1-i, 2) use the following spinor X=A(1,2-i).
(a) Please use normalization to find A.
(b) What values of Sz could you get? What is the probability of each? What is the expectation value of Sz?
(c) Same for Sx
(d) Same for Sy.

Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

2D Harmonic Oscillator and Spin

This is only a preview of the solution. Please use the purchase button to see the entire solution

Assisting Tutor

Related Homework Solutions

Get help from a qualified tutor
Live Chats