{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# ps8 - Harvard University Physics 143b Quantum Mechanics II...

This preview shows pages 1–2. Sign up to view the full content.

Harvard University Physics 143b: Quantum Mechanics II Problem Set 8 due Friday November 19 1. Consider non-relativisitic electrons constrained to move on a thin ring of radius R . Assuming we can ignore motion except along the angular direction of the ring, which is labelled by an angle θ , the Schr¨odinger equation for the wavefunction ψ ( θ ) is - ¯ h 2 2 mR 2 d 2 ψ 2 = Eψ. (1) The eigenfunctions are ψ = e i‘θ / 2 π , and the eigenenergies are ¯ h 2 2 / (2 mR 2 ), where is any integer. Now magnetic flux Φ is inserted in the center of the ring. (a) The vector potential can be chosen to have only an angular component. Show that A θ = Φ / (2 πR ), and so the Schr¨ odinger equation is modified to 1 2 mR 2 ¯ h i d - q Φ 2 π ! 2 ψ = (2) where q is the charge of the electron. (b) List the eigenvalues of (2). (c) Plot the total ground state energy of 5 electrons as a function of Φ (ignore electron spin, and you can use Mathematica if you wish).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

ps8 - Harvard University Physics 143b Quantum Mechanics II...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online