This is (another!) question I cannot solve(adsbygoogle = window.adsbygoogle || []).push({});

The ground state wavefunction for the harmonic oscillator can be written as

[tex]$\chi _0 = \left( {\frac{\alpha }

{\pi }} \right)^{\frac{1}

{4}} \exp \left( {\frac{{ - \alpha x^2 }}

{2}} \right)$

[/tex]

where [tex]$\alpha = \sqrt {\frac{{mk}}

{{\hbar ^2 }}} $

[/tex]

We are then asked to apply the rasing operator:

d/dy-y

where [tex]$y = \sqrt \alpha x$

[/tex]

First of all, does this mean replace all alphas, and x's with y's? (Is it even possible to get rid of all x's? I end up with a y/x in there), and then apply

d(chi)/dy-y*chi

Is that what the operator is doing? I don't see the significane of the answer. If I apply the lowering operator (d/dy + y) I still get 'an' answer, when I figure I should get something to tell me I can't go lower then the groud state (a zero perhaps, or a mathematical impossibility like division by zero)

Anyway...if anyone can shed some light on this it would eb much appreciated!

Edit: I cant figure out division on this board! I swear to god I am doing it right...I will post my operator down here...if someone can point out the latex error I'd love to know:

[tex]\[

\frac{d}

{{dy}} - y

\]

[/tex]

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# Raising Operator (Harmonic Oscillator)

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