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leoflindall
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Homework Statement
Write down the time independant schrodinger equation in the momentum representation for a particle with mass m when the potential is given by V (x) = 1/2 [tex]\gamma[/tex] x2.
A possible soloution of this schrodinger equation is of the form
[tex]\Psi[/tex] (p) = Ae-Bp2 / 2
Determine B and the corresponding energy eigenvalue.
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Homework Equations
The Attempt at a Solution
I think the schrodinger equation is
[tex]\frac{p2}{2m}[/tex] [tex]\Psi[/tex] (r) - 1/2 [tex]\gamma[/tex] [tex]\hbar[/tex]2 d2/dx2 [tex]\Psi[/tex] (r) = E [tex]\Psi[/tex] (r)
Where i have used the momentum representation p = p . x = -ih d/dx.
Is this correct?
Secondly how do approach determing B, and find the energy eigenvalue?
Do i need to solve the equation directly, possibly by using separation of vartiables?
Many thanks for any advice or help.
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