let be a particle in a potential well with mass m=1/2 so we have the equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex](p^{2}+V(x))\phi=E_{n}\phi [/tex]

we don,t know if V is real or complex but we have that if En is an energy,its complex conjugate En^*=Ek is also another energy of the system,my question is if the potential is real...

Proof?:taking normalized Eigenfunctions of the Hamiltonian....with [tex]<\phi|\phi>=1 [/tex] then we would have:

[tex](<\phi_{n}|T+V|\phi_{n}>)^{*}=(<\phi_{k}|T+V|\phi_{k}>)[/tex]

so in the end separating and knowing that [tex]<\phi|p^{2}|\phi> [/tex] is always real then we would have that:

[tex]\int_{-\infty}^{\infty}|\phi_{n}|^{2}V^*(x)-int_{-\infty}^{\infty}|\phi_{k}|^{2}V(x)=r [/tex] with r a real number....

so we would have for every k and n and complex part of the potential b(x) that:

[tex]} (|\phi_{n}|^{2}+|\phi_{k}|^{2})b(x)dx=0 [/tex]

so the complex part of the potential is 0...is that true?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Particle on a potential well

**Physics Forums | Science Articles, Homework Help, Discussion**