PHY-852 QUANTUM MECHANICS II
Homework 6, 40 points
February 23 - March 2, 2011
Identical particles
Reading: Quantum Physics, Volume 2, Sections 15.1-4, 17.1-4, 18.1-3
1. /10/ a. Consider a system of t
PHY-852: QUANTUM MECHANICS II
Quiz 2
February 4, 2011
NAME.
PROBLEM. For the following operators find out if they correspond to conserved quantities for free motion of a relativistic particle of spin
Variational method and diagonalization
Take a complete orthonormalized set of states |ni. Select N states of this
set, |1i, |2i, ., |N i, and look for the approximate solution of the stationary
Schr
o
PHY-852: QUANTUM MECHANICS II
Quiz 5
March 18, 2011
NAME.
PROBLEM. Consider a neutron in the gravitational field near the surface
of the Earth. Estimate the energy of its quantum ground state using th
Phys 852, Quantum mechanics II, Spring 2009
Time-Independent Perturbation Theory
Prof. Michael G. Moore, Michigan State University
1
The central problem in time-independent perturbation theory:
Let H0
PHYS852 Quantum Mechanics II, Spring 2010
HOMEWORK ASSIGNMENT 9: Solutions
Topics covered: hydrogen hyper-ne structure, Wigner-Ekert theorem, Zeeman eect
1. Relations between V and J : For a rotation
PHYS852 Quantum Mechanics II, Spring 2010
HOMEWORK ASSIGNMENT 8: Solutions
Topics covered: hydrogen ne structure
1. [10 pts] Let the Hamiltonian H depend on the parameter , so that H = H (). The eigen
PHYS852 Quantum Mechanics II, Spring 2010
HOMEWORK ASSIGNMENT 8
Topics covered: hydrogen ne structure
1. [10 pts] Let the hamiltonian H depend on the parameter , so that H = H (). The eigenstates and
PHYS852 Quantum Mechanics II, Spring 2010
HOMEWORK ASSIGNMENT 7: Solutions
Topics covered: addition of three angular momenta, degenerate perturbation theory
1. Consider a system of two spin-1/2 partic
PHYS852 Quantum Mechanics II, Spring 2010
HOMEWORK ASSIGNMENT 7
Topics covered: addition of three angular momenta, degenerate perturbation theory
1. Consider a system of two spin-1/2 particles, descri
PHY-852: QUANTUM MECHANICS II
Quiz 7
April 1, 2011
NAME.
PROBLEM. A particle of mass m and electric charge e is placed in the onedimensional harmonic oscillator potential of frequency . The uniform el
PHY-852: QUANTUM MECHANICS II
Quiz 6
March 25, 2011
NAME.
PROBLEM. A quantum harmonic oscillator with mass m and elastic force
kx is perturbed by a small change k k + . Using perturbation theory
find
PHY-852: QUANTUM MECHANICS II
Quiz 3
February 11, 2011
NAME.
PROBLEM. Consider two Hamiltonians of a non-relativistic particle of
spin 1/2 which consist of kinetic energy, spin-independent central pot
PHY-852: QUANTUM MECHANICS II
Quiz 1
January 28, 2011
NAME.
PROBLEM. a. Calculate the mixed product of three Pauli matrices
A = ~ [~ ~ ] .
(1)
b. Reduce to the form linear with respect to the Pauli ma
PHY-852: QUANTUM MECHANICS II
Quiz 4
February 18, 2011
NAME.
PROBLEM. A proton state is characterized by the momentum p along the
z-axis and by the certain value h = +1 of the helicity [projection h =
PHY-852 QUANTUM MECHANICS II
Midterm test
March 4, 2011
Total 30 points
NAME.
1. Write down the Dirac equation for a particle moving in a spherically symmetric electrostatic potential (r). List all co
PHYS852 Quantum Mechanics II, Spring 2010
HOMEWORK ASSIGNMENT 6: Solutions
Topics covered: Time-independent perturbation theory.
1. [30] Two-Level System: Consider the system described by H = Sz + Sx
PHYS852 Quantum Mechanics II, Spring 2010
HOMEWORK ASSIGNMENT 6
Topics covered: Time-independent perturbation theory.
1. [30] Two-Level System: Consider the system described by H = Sz + Sx , with > 0,
QUANTUM MECHANICS SUBJECT EXAM Spring 2008 ID NUMBER:
1. POSTULATES OF QUANTUM MECHANICS: A certain quantum system is governed by th energy eigenstate of the Hamiltonian H = n=0 En |n n|, where the st
Phys 852, Quantum mechanics II, Spring 2009
Time-Independent Perturbation Theory
Prof. Michael G. Moore, Michigan State University
Atomic Physics Applications
1
Introduction
For many reasons it is imp