Shankar 163(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Show that for any normalized |psi>, <psi|H|psi> is greater than or equal to E_0, where E_0 is the lowest energy eigenvalue. (Hint: Expand |psi> in the eigenbasis of H.)

2. Relevant equations

3. The attempt at a solution

I think the question assumes the V = 0, so H = P^2/2m. The eigenvalues for the equation P^2/2m|p> = E|p> are then p = +/- (2mE)^(1/2) and the eigenkets are of the form | p = + (2mE)^(1/2)> and | p = (2mE)^(1/2)> (or in energy terms the eigenvalues are of the form |E,->, |E,+> and the eigenkets are the same as the momentum ones. I'm not really sure how you can expand anything with these though...

**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: The lowest energy eigenvalue

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