Consider the one-dimensional wave function (x) = A(x/x0)" e-=/20 , %3D where A, n and xo are constants. (a) Using Schrödinger's equation, find the potential V (x) and energy E for which this wave function is an eigenfunction. (Assume that as I → 00, V (x) → 0). (b) What connection do you see between this potential and the effective radial potential for a hydrogenic state of orbital angular momentum l?
Consider the one-dimensional wave function (x) = A(x/x0)" e-=/20 , %3D where A, n and xo are constants. (a) Using Schrödinger's equation, find the potential V (x) and energy E for which this wave function is an eigenfunction. (Assume that as I → 00, V (x) → 0). (b) What connection do you see between this potential and the effective radial potential for a hydrogenic state of orbital angular momentum l?
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Transcribed Image Text:Consider the one-dimensional wave function
v(x) = A(x/x0)" e-=/20 ,
%3D
where A, n and xo are constants.
(a) Using Schrödinger's equation, find the potential V(x) and energy E
for which this wave function is an eigenfunction. (Assume that as I -→ 00,
V (x) → 0).
(b) What connection do you see between this potential and the effective
radial potential for a hydrogenic state of orbital angular momentum l?
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