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indie452
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Homework Statement
Particle mass m is confined by a one dimensional simple harmonic oscillator potential V(x)=Cx2, where x is the displaecment from equilibrium and C is a constant
By substitution into time-independant schrodingers with the potential show that
[tex]\psi[/tex](x)=Axe-ax2
is a possible spatial wavefunction for this particle provided constant a has a certain value.
Find a in term os C, m, h bar (\h)
What the corresponding energy eigen value
The Attempt at a Solution
[tex]\psi[/tex](x)= Axe-ax2
d/dx [tex]\psi[/tex](x)= [A - 2Aax2]*e-ax2
d2/d2x [tex]\psi[/tex](x)= [4a2Ax3 - 6aAx]*e-ax2
so shrodingers:
[tex]\frac{-hbar^2}{2m}[/tex]*[4a2x2 - 6a] + Cx2 = E
Ive gotten to this bit but i don't understand what to do, i have read the 4 page solution in Eisburg&Resnick and spoke to my lecturer, but my lecturer has said that i don't need to do the long winded complete solution and that i is also not necessary to evaluate the normalisation constant A.
I just don't know how to show that the psi above is a possible wavefunction
help or advice on how to do this problem would be much appreciated
ps I have tried looking at and doing some other example but they all had the potential as V(x)= 1/2 Cx2, this seemed to be the standard example. I also tried using the substitution w2= (c/m) and this would give a potential V(x)= mw2x2, but i didnt know if this was right as the question ask for a in terms of C (and m and hbar)
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