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naggy
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Homework Statement
If [tex]U[/tex] is an operator so [tex]U\Psi(x)[/tex] = [tex]\Psi(x-a)[/tex].
How can I show that [tex]exp(-iaP/h) = U[/tex]
where P is the momentum operator [tex]P = -ih(d/dx)[/tex]
Homework Equations
Not sure
The Attempt at a Solution
What I do know that if I have a function F of an operator then
[tex]F(P)\psi[/tex] = [tex]$\sum_{i} c_iF(\lambda_i)\psi_i[/tex]
where [tex]\lambda_i[/tex] are the eigenvalues of [tex]P[/tex]
and [tex]c_i = <\psi_i,\psi>[/tex]
can I somehow relate all of this to the operator [tex]U[/tex]