Question

Two electrons are in a one-dimensional box, and have the individual 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 functions for the two electrons. (Explain what principle you are using to determine the answer, and why your answer satisfies this principle.) [10 pts]

(b) Next suppose that the electrons have the individual 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 total wavefunction(s) with total spin s = 1 ? Again, explain your reasoning. [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 an electron, but the other particle is a muon - a particle which has the same spin and charge as an electron, but a larger mass. One particle has an individual wavefunctionψ ( x 1 ) = 2 L sin ⁡ ( π x 1 / 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].

Answer 1