Thermodynamics, Statistical Physics, and Quantum Mechanics

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5.71 Attractive Delta Function in 3D (Princeton)

A particle moves in threedimensions. The onlypotential is an attractive

deltafunction at of the form

whereDis a parameter which determines the strength of thepotential.

a)

b)

What are thematchingconditions at for the wavefunction and

its derivative?

For what values ofDdo boundstates exist for

5.72 Ionizing Deuterium (Wisconsin-Madison)

The hydrogenatom has an ionization energy of when an
electron is bound to aproton. Calculate theionization energy ofdeuterium:
an electron bound to a deuteron. Give youranswer as thedifferencebetween
the binding energy of deuterium andhydrogen The
deuteron has unitcharge. Thethreemasses are, in atomicmass units,

5.73 Collapsed Star (Stanford)

In a very simple model of acollapsedstar alarge number of
nucleons (N neutrons and protons) and electrons (to ensure electric
neutrality) areplaced in aone-dimensionalbox (i.e., an infinitesquare
well) oflength The neutron andproton have equalmass and
the electron hasmass Assume the nucleon numberdensity is
neglect allinteractions between the
particles in thewell, and approximate

Whichparticlespecies arerelativistic?

Calculate thegroundstate energy of the system as afunction of

for all possible configurations with fixed A.

What value of (assumed small)minimizes the totalenergy of the

system?

a)

b)

c)

PROBLEMS