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**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=m**

_{1}m_{2}/(m_{1}+m_{2}). An object of mass m_{2}and charge -e orbits an object of mass m_{1}and charge +Ze. By appropriate substitutions into formulas given in the chapter, show that a) the allowed energies are : (Z^{2}μ/m)E_{1}/n^{2}, where E_{1}is the hydrogen ground state, and b) the "bohr radius" for this system is (m/Zμ)a_{0}, where a_{0}is the hyrogen bohr radius## Homework Equations

E

_{n}= -me

^{4}/2(4πε

_{0})

^{2}hbar

^{2}(1/n

^{2}); n=1,2,3....

L=[itex]\sqrt{l(l+1)}[/itex]hbar

L

_{z}=m

_{L}hbar ; m

_{L}=...-2,-1,0,1,2,...

-hbar

^{2}/2m(∇

^{2}ψ(r) + U(r)ψ(r)= Eψ(r)

U(r)= -1/(4πε

_{0})(Ze)(e)/r ---->

E

_{n}= - me

^{4}Z

^{2}/2(4πε

_{0})

^{2}hbar

^{2}*(1/n

^{2})

NOTE: hbar= plancs constant divided by 2 pi.

## 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.