I have to find the allowed energies of this potential:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\[V(x)=

\begin{cases}

\frac1{2}m\omega^2x^2 & \text{for } x > 0\\

\infty & \text{for } x < 0

\end{cases}

\]

[/tex]

My suggestion is that all the odd-numbered energies (n = 1, 3, 5...) in the ordinary harmonic osc. potential are allowed since [tex]\psi(0) = 0[/tex] in the corresponding wave functions and this is consistent with the fact that [tex]\psi(x)[/tex] has to be 0 where the potential is infinite.

In the assignment it says that it takes some careful thought to reach this result and it took me 10 seconds to figure this out. In other words; somethings is wrong :tongue2:

PS. I am new to quantum mechanics so please don't use any obscure notation

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# Homework Help: Half-harmonic oscillator potential

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