Consider a one-dimensional potential prole in spherical coordinates given by V (

Question

Consider a one-dimensional potential prole in spherical coordinates given
by
V (r) = -25 r < R;
V (r) = 15 R < r < 2R;
V (r) = 0 2R < r:

a) For what range of energies are bound states allowed?
b) Do the eigenfunctions for this problem have parity proper-
ties? If so, sketch the shape of an eigenfunction pertinent to this potential
with even parity and sketch an eigenfunction shape with odd parity.
c) Consider a beam of particles launched from R = 1 with
energy E > 0. For what range of energies E is the re
ection coecient R = 1?

Explanation / Answer

a) E<25

b) even - cos(r/R)

odd - sin(r/r)

c) what do you mean by reaction coefficient, there are many meanings of that term

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