Solutions to HW4
Quantum Physics II, Fall 2012
September 27, 2012
Q1 :
The z-component of the spin of an electron is measure and the value 2 is found. Immediately
afterwards, the spin along a direction making an angle with the z-axis is measured. What are
Quantum Physics II, Phys402, Fall 2012
Instructor: Prof. Bedaque
Nov. 14th, 2012
TA: [email protected]
Solution #9
Question A: Variational Calculation for the Anharmonic Oscilator
Answer:
p2
x2
; H = 2m + x4
e
1
Doing simple integral, we get A=( 2 ) 4
Fir
Quantum Physics II, Phys402, Fall 2012
Instructor: Prof. Bedaque
Nov. 6th, 2012
TA: [email protected]
Solution #8
Question A: ANHARMONIC OSCILLATOR
Answer:
1. We choose the basis of eigenstates of the standard harmonic oscillator.
1
2. Using raising and low
Quantum Physics II, Phys402, Fall 2012
Instructor: Prof. Bedaque
Oct. 26th, 2012
TA: [email protected]
Solution #7
Question A: Perturbation Theory for the Anharmonic oscillator
p2
!2
The anharmonic oscillator is described by the hamiltonian H = 2m + m2 x2 +
Quantum Physics II, Phys402, Fall 2012
Instructor: Prof. Bedaque
Oct. 12nd, 2012
TA: [email protected]
Solution #6
Question A:
Consider two identical spin-12 fermions in an external harmonic oscillator potential. There
is no interaction between the fermions
Solutions to HW5
Quantum Physics II, Fall 2012
Oct. 3rd, 2012
Question A:
A spin lees particle moves in one dimension and, at some instant, is described by the wave function
(x) = hx| | i. At that instant the momentum of the particle is measured. What are