# Condensed matter physics

1. Nov 20, 2011

### helpcometk

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

1. Consider two protons, separated by a distance R, and one electron. Assume
that the electron wave function can be symmetric, s, or asymmetric, a, with:
ψs = Ns( ψ1 + ψ2);
ψa = Na( ψ1 - ψ2):
Here 1 and 2 are the electron wave functions for large R when bound with
proton 1 or proton 2, respectively
a) Derive a expression for the normalisation constants Ns and Na. [6 Marks]
b) Assuming the Hamiltonian is given by:

look image attachment

where r1 and r2 are the distances to proton 1 and proton 2, respectively.
Derive an expression for the energies Es and Ea.

2. Relevant equations

for a) i found a solution here : http://farside.ph.utexas.edu/teaching/qmech/lectures/node129.html#e14.57

is this correct ?

im still confused with energues Ea and Eb

3. The attempt at a solution

#### Attached Files:

• ###### hamiltonian.bmp
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