Deriving Wave Function: Confused about (ix/a) & (-x^2/2a)?

sus1234
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Homework Statement
Trying to understand how the time independent wavefunction is derived from this
Relevant Equations
?
1644783404516.png


It is asking to derive the time-independent wave function and has managed to get the answer of
1644783451034.png

and i am very confused as where (ix/a) and (-x^2/2a) came from ?

Thanks.
 
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The answer's wrong.

First, change variables to ##k' = k-k_0##, and then complete the square.
 
vela said:
The answer's wrong.

First, change variables to ##k' = k-k_0##, and then complete the square.
Hi,

Thank you for your reply, I'm not sure where I'm meant to sub in k' = k-k0, could you provide more guidance ?

thanks
 
sus1234 said:
Thank you for your reply, I'm not sure where I'm meant to sub in k' = k-k0, could you provide more guidance ?
You've never changed the variable of integration?
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
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Thread 'Number of quantum accessible states of a particle given T, N?'

It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and ##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate ##g(\epsilon)## and we have...
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