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 A particle of mass is placed in a finite spherical
well:
with and .
Find the groundstate by solving the radial equation with .
Show that there is no groundstate if
.
 Consider a particle of mass in the threedimensional harmonic oscillator potential
. Solve the problem by separation of
variables in spherical polar coordinates, and, hence, determine the
energy eigenvalues of the system.
 The normalized wavefunction for the groundstate of a hydrogenlike
atom (neutral hydrogen, , , etc.) with
nuclear charge has the form
where and are constants, and is the distance between the
nucleus and the electron. Show the following:

.
 , where
.
 The energy is where
.
 The expectation values of the potential and kinetic energies are
and , respectively.
 The expectation value of is
.
 The most probable value of is .
 An atom of tritium is in its groundstate. Suddenly the nucleus
decays into a helium nucleus, via the emission of a fast electron
which leaves the atom without perturbing the extranuclear electron,
Find the probability that the resulting ion will be
left in an , state. Find the probability that it will
be left in a , state. What is the probability that the
ion will be left in an state?
 Calculate the wavelengths of the photons emitted from the , to ,
transition in hydrogen, deuterium, and positronium.
 To conserve linear momentum, an atom emitting a photon must
recoil, which means that not all of the energy made available in the
downward jump goes to the photon. Find a hydrogen atom's recoil
energy when it emits a photon in an to transition. What
fraction of the transition energy is the recoil energy?
Next: Spin Angular Momentum
Up: Rydberg Formula
Previous: Rydberg Formula
Richard Fitzpatrick
20100720