Thermodynamics, Statistical Physics, and Quantum Mechanics

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function is at thecenter of the box.

a)

b)

c)

What are theeigenvalues ofodd-paritystates?

Find the value ofCfor which thelowesteigenvalue iszero.

Find the ground state wave function for thecase that the lowest

eigenvalue islessthanzeroenergy.

5.8 Particle inExpanding Box (Michigan State, MIT,

Stony Brook)

A particle ofmassmis contained in a one-dimensionalimpenetrable box

extendingfrom The particle is in its ground state.

a)

b)

Find the eigenfunctions of the ground state and the firstexcitedstate.

The walls of thebox are movedoutward instantaneously toform a

box extending from Calculate the probability that the

particle will stay in the ground state duringthissudden expansion.

Calculate the probabilitythat the particlejumps from the initial

groundstate to the firstexcitedfinal state.

5.9 One-Dimensional Coulomb Potential (Princeton)

An electronmoves in onedimension and is confined tothe right half-space

where it has a potential energy

whereeis the charge on anelectron. Thisis the imagepotential of an

electron outside aperfect conductor.

Find the ground stateenergy.

Find the expectation value in thegroundstate

5.10 Two Electrons in a Box (MIT)

Two electrons areconfined in one dimension to a box oflength Aclever

experimentalist has arrangedthat bothelectrons have thesame spinstate.

Ignore the Coulomb interactionbetween electrons.

a) Write the ground state wave function for thetwo-electron

system.

b) What is the probability that bothelectrons arefound in thesame

half of the box?

c)

a)

b)

QUANTUM MECHANICS