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thepopasmurf
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I'm trying to teach myself quantum mechanics using a book I got. I made an attempt at one of the questions but there are no solutions or worked examples so I'm wondering if I got it right.
Here it goes
Suppose an observable quantity corresponds to the operator \hat{B}= -\frac{\hbar^2}{2m}\frac{d^2}{dx^2}.
For a particular system, the eigenstates of this operator are
\Psi(x)=Asin\frac{n\pi x}{L}, where n = 1,2,3,...; A is the normalisation constant
Determine the eigenvalues of \hat{B} for this case
\hat{A}\psi_{j}=a_{j}\psi_{j} I think
I used the operator on \psi and differenciated twice to get
\frac{\hbar^2 n^2 \pi^2}{2mL^2}ASin\frac{n\pi x}{L}
this corresponds to a_j\psi_j so my answer for the eigenvalues is
\frac{\hbar^2 n^2 \pi^2}{2mL^2}
This is my first attempt at anything like this so any help is welcome
Here it goes
Homework Statement
Suppose an observable quantity corresponds to the operator \hat{B}= -\frac{\hbar^2}{2m}\frac{d^2}{dx^2}.
For a particular system, the eigenstates of this operator are
\Psi(x)=Asin\frac{n\pi x}{L}, where n = 1,2,3,...; A is the normalisation constant
Determine the eigenvalues of \hat{B} for this case
Homework Equations
\hat{A}\psi_{j}=a_{j}\psi_{j} I think
The Attempt at a Solution
I used the operator on \psi and differenciated twice to get
\frac{\hbar^2 n^2 \pi^2}{2mL^2}ASin\frac{n\pi x}{L}
this corresponds to a_j\psi_j so my answer for the eigenvalues is
\frac{\hbar^2 n^2 \pi^2}{2mL^2}
This is my first attempt at anything like this so any help is welcome
