A zero-spin, q-charged, mass m particle is constrained to move in the xy-plane and at the 2-dimensional harmonic oscilla
Posted: Wed May 18, 2022 4:16 pm
A zero-spin, q-charged, mass m particle is constrained to move
in the xy-plane and at the 2-dimensional harmonic oscillator
potential:
a) Find the eigenvalues and eigenvectors of H0 using
the creation and destruction operators for each dimension, i.e. by
defining (a, a†) for x and (b, b†) for y. Write down the energy and
eigenvectors of the second excited state.
b) If this particle is moving in a weak magnetic field B = Bˆz,
the following term is added to the Hamiltonian operator:
Taking the H′ term as perturbation;
QUANTUM MECHANICS II - PERTURBATION THEORY
1 1 Но (P% + p?;) + 5 mw? (x2 + y2) + ? + ? + ? — 2m 2
9 H' = -M. B = - L·B 2m = = . = qB (xPy – ypa) 2m
B = B2
in the xy-plane and at the 2-dimensional harmonic oscillator
potential:
- A Zero Spin Q Charged Mass M Particle Is Constrained To Move In The Xy Plane And At The 2 Dimensional Harmonic Oscilla 1 (5.9 KiB) Viewed 49 times
the creation and destruction operators for each dimension, i.e. by
defining (a, a†) for x and (b, b†) for y. Write down the energy and
eigenvectors of the second excited state.
b) If this particle is moving in a weak magnetic field B = Bˆz,
the following term is added to the Hamiltonian operator:
Taking the H′ term as perturbation;
- A Zero Spin Q Charged Mass M Particle Is Constrained To Move In The Xy Plane And At The 2 Dimensional Harmonic Oscilla 2 (7.57 KiB) Viewed 49 times
1 1 Но (P% + p?;) + 5 mw? (x2 + y2) + ? + ? + ? — 2m 2
9 H' = -M. B = - L·B 2m = = . = qB (xPy – ypa) 2m
B = B2