# Solid-State and molecular physics; allowed energy states

1. Jan 20, 2014

### mjmontgo

When two objects move under the influence of their mutual force alone, we can treat the relative motion as a one-particle system of mass μ=m1m2/(m1+m2). An object of mass m2and charge -e orbits an object of mass m1 and charge +Ze. By appropriate substitutions into formulas given in the chapter, show that a) the allowed energies are : (Z2μ/m)E1/n2, where E1 is the hydrogen ground state, and b) the "bohr radius" for this system is (m/Zμ)a0, where a0 is the hyrogen bohr radius

2. Relevant equations

En= -me4/2(4πε0)2hbar2(1/n2); n=1,2,3....

L=$\sqrt{l(l+1)}$hbar

Lz=mLhbar ; mL=...-2,-1,0,1,2,...

-hbar2/2m(∇2ψ(r) + U(r)ψ(r)= Eψ(r)

U(r)= -1/(4πε0)(Ze)(e)/r ---->
En= - me4Z2/2(4πε0)2hbar2*(1/n2)

NOTE: hbar= plancs constant divided by 2 pi.

3. The attempt at a solution

Im at a standstill just starting this problem, i know its a long shot asking for help. But if anyone looks at this and has an idea it would be greatly appreciated. Just looking and playing around with substitution i did not get anything close... even some insight or ideas would be great thanks.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution