Particle in an Infinite Spherical Well

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A particle of mass in an infinite spherical potential well of radius
is described by the Schrödinger equation
. The wavefunction is separable in spherical polar coordinates, such that
, where
is a spherical harmonic,
a spherical Bessel function, and
is a normalization constant. The boundary condition that
at
is fulfilled when
is the
zero of the spherical Bessel function
. The quantized energy levels are then given by
and are
-fold degenerate with
. The conventional code is used to label angular momentum states, with
representing
. Unlike atomic orbitals, the
-values are not limited by
; thus one will encounter states designated
, etc.
Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshots 1–3: the three lowest energy states
Snapshot 4: energy-level diagram
Permanent Citation