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Two electrons are in a one-dimensional box, and have the individual wavefunctions ψ ( x 1...

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Physics

Two electrons are in a one-dimensional box, and have theindividual wavefunctions ψ ( x 1 ) = 2 L sin ⁡ ( π x 1 / L ) , ψ (x 2 ) = 2 L sin ⁡ ( π x 2 / L )

(a) Determine the possible total wave functionsfor the two electrons. (Explain what principle you are using todetermine the answer, and why your answer satisfies thisprinciple.) [10 pts]

(b) Next suppose that the electrons have theindividual wavefunctions ψ ( x 1 ) = 2 L sin ⁡ ( π x 1 / L ) , ψ (x 2 ) = 2 L sin ⁡ ( 2 π x 2 / L ). What are the possible totalwavefunction(s) with total spin s = 1 ? Again, explain yourreasoning. [10 pts]

(c) In the same situation as in part (b),determine the possible total wavefunction(s) with total spin s = 0.[5 pts]

(d) Now suppose that one of the particles is anelectron, but the other particle is a muon - a particle which hasthe same spin and charge as an electron, but a larger mass. Oneparticle has an individual wavefunctionψ ( x 1 ) = 2 L sin ⁡ ( π x1 / L ) while the other has an individual wavefunction ψ ( x 2 ) =2 L sin ⁡ ( π x 2 / L ).

Does the exclusion principle determine the total wavefunction?Explain why or why not. [5 pts].

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