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Hello,

I am trying to express a given wavefunction through different basis, momentum and position. Look at 5.2(b) and (c) through the link: http://qis.ucalgary.ca/quantech/443/2011/homework_five.pdf" [Broken]

I complete part (b) by doing the following:

[tex]\int\left\langle{x}\left|e^{\frac{-i\hat{p}a}{h}}\left|{x'}\right\rangle\left\langle{x'}\left|\psi\right\rangle dx' = \psi(x+a)[/tex]

If I did part (b) correctly, then for part (c), I did the same thing to find the state in the momentum basis:

[tex]\int\left\langle{p}\left|e^{\frac{-i\hat{p}a}{h}}\left|{p'}\right\rangle\left\langle{p'}\left|\psi\right\rangle dp' = \int e^{\frac{-ip'a}{h}}\psi(p')dp'[/tex]

Now I do not know where to go..and I do not know if i did the right steps.

So if anyone can help, that would be great!

Thank You

Doublemint

Edit:

I have looked at 5.3(b) and the integration is horrible...

Given that: [tex]\tilde{\psi}(p) = \frac{1}{\sqrt{2\pi\hbar}}\int\psi(x)e^{\frac{-ipx}{\hbar}}dx = \frac{1}{\sqrt{2\pi\hbar}}\int Axe^{\frac{-k^{2}x^{2}}{2}}e^{\frac{-ipx}{\hbar}}dx[/tex]. Any one got ideas on this one as well?

I am trying to express a given wavefunction through different basis, momentum and position. Look at 5.2(b) and (c) through the link: http://qis.ucalgary.ca/quantech/443/2011/homework_five.pdf" [Broken]

I complete part (b) by doing the following:

[tex]\int\left\langle{x}\left|e^{\frac{-i\hat{p}a}{h}}\left|{x'}\right\rangle\left\langle{x'}\left|\psi\right\rangle dx' = \psi(x+a)[/tex]

If I did part (b) correctly, then for part (c), I did the same thing to find the state in the momentum basis:

[tex]\int\left\langle{p}\left|e^{\frac{-i\hat{p}a}{h}}\left|{p'}\right\rangle\left\langle{p'}\left|\psi\right\rangle dp' = \int e^{\frac{-ip'a}{h}}\psi(p')dp'[/tex]

Now I do not know where to go..and I do not know if i did the right steps.

So if anyone can help, that would be great!

Thank You

Doublemint

Edit:

I have looked at 5.3(b) and the integration is horrible...

Given that: [tex]\tilde{\psi}(p) = \frac{1}{\sqrt{2\pi\hbar}}\int\psi(x)e^{\frac{-ipx}{\hbar}}dx = \frac{1}{\sqrt{2\pi\hbar}}\int Axe^{\frac{-k^{2}x^{2}}{2}}e^{\frac{-ipx}{\hbar}}dx[/tex]. Any one got ideas on this one as well?

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