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Shrodinger Equation for Multiple Particles

  • #1

Homework Statement



Five identical non-interacting particles are placed in an infinite square well with width L = 1 nm. I am asked to find the energy of the system if the particles are electrons.

Homework Equations



The time-independent Schrodinger equation for a system of two particles, both with the same mass 'm' is:

-h(bar)2/2m * (d2[tex]\psi[/tex](x1x2 / (d2x21)) - h(bar)2/2m * (d2[tex]\psi[/tex](x1x2) / (d2x22)) + V[tex]\psi[/tex](x1x2) = E[tex]\psi[/tex](x1x2)

All derivatives are partials.

Also, energy En = -13.6(Z2 / n2)eV.

The Attempt at a Solution



Alright so since the question specifies the particles do not interact, V = V1(x1) + V2(x2). As in regular Schrodinger equations, I want to solve where V = 0 and I can write [tex]\psi[/tex]nm(x12) = [tex]\psi[/tex]n(x1)[tex]\psi[/tex]m(x2). From here I'm stuck -- how do I solve for a system of five particles, and how do I find the energy from here?

(sorry for the typo in the title, by the way)
 

Answers and Replies

  • #2
674
2
Do you know how to solve it for a system of 2 noninteracting particles? It is treated exactly the same way for 5 particles.
 

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