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Two electrons are confined in an extremely thin wire of length a. You may treat this wire as a one-dimensional infinite potential well. A clever experimentalist has arranged that both electrons have the same spin state. Ignore the Coulomb interaction between the electrons. Denote the electron mass by m.

A). What is the ground state wave function \(\psi(x1,x2)\) for the two-electron system?

B.) What is the energy of the ground state?

C.) What is the probability that both electrons are found in the left half of the box?

D.) Based on your answer to part (c), what is the probability of finding one electron on the left half and the other electron on the right half of the box?

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