The Central Potential
The 3-D time independent Schrodinger equation for a particle of mass m in a spherically symmetric potential is
a) By writing grad^ in terms of r, theta and phi show that this can be written as
(b) Writing shi = R Y show that Y must satisfy L^2 Y = c Y where c is a constant, and where
(c) Writing R = f(r)/r, show that f(r) satisfies the equation
(d) This is of exactly the same form as a 1-D time independent Schrodinger equation with V replaced by V + c/2mr^2. So can we conclude that the spectrum in the original 3D problem is the same as for this 1D problem?© BrainMass Inc. brainmass.com March 4, 2021, 8:30 pm ad1c9bdddf
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