Thermodynamics, Statistical Physics, and Quantum Mechanics

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b) What is theeigenvalue of theground state?

c)At time anelectric field isswitched on,adding aperturba-

d) Assuming that the field is switched on in atime much faster than

what is theprobabilitythat the particlestays in theground state?

5.21 Cut the Spring! (MIT)

A particle isallowed to move inone dimension. It is initially coupled to
two identicalharmonic springs,each withspring constant K. The springs
are symmetricallyfixed to thepoints sothat when theparticle is at
the classical force on it is zero.

a) What are theeigenvalues of theparticle while itis connected toboth

springs?

b) What is thewavefunction in the ground state?

c) One spring is suddenlycut, leaving theparticlebound toonly the

other one. If the particleis in thegroundstatebefore the spring is

cut, what is theprobability it is still in theground state after the

spring is cut?

Angular Momentum and Spin

5.22 Given Another Eigenfunction (Stony Brook)

A nonrelativistic particle of mass moves in athree-dimensional central
potential whichvanishes at We are given that an exact
eigenstate is

whereCand are constants.

a)

b)

c)

What is theangularmomentum of this state?

What is the energy?

What is

5.23 Algebra of Angular Momentum (Stony Brook)

Given the commutator algebra

PROBLEMS

tion of theform What is the newground stateenergy?