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kini.Amith
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Homework Statement
The wave function ψ(x)=Ae-b2x2/2 where A and b are real constants, is a normalized eigenfunction of the schrodinger eqn for a free particle of mass m and energy E. Then find the value of E
Homework Equations
The Attempt at a Solution
Substituting the wave function in the time independent schrodinger equation in 1D for free particle (V(x)=0), I got
[tex]E=\frac{\hbar^2 b^2 (1-b^2 x^2)}{2m}[/tex]
But i thought eigenvalues should not contain the variable x and i don't know how to get rid of it. Apparently, the correct answer is
[tex]E=\frac{\hbar^2 b^2 }{2m}[/tex]
which is obtained by taking x=0 in my answer. But how can i simply substitute x=0?