Consider a pne dimensional infinite-wall potential Vo for > L and <0, and V-0 for OAKL There are two identical spin half fermions in this potential well and spin states are denowed by) and 4) for spin up and down, respectively. a) (Very ensy) Find the eigenvalues and the corresponding wave functions for the potential well. b) (Ensy) Write the full wave function for the fermions in singlet state with possible minimum energy. e) (Easy) Write the full wave function for the fermions in triplet state with possible minimum energy.
Consider a pne dimensional infinite-wall potential Vo for > L and <0, and V-0 for OAKL There are two identical spin half fermions in this potential well and spin states are denowed by) and 4) for spin up and down, respectively. a) (Very ensy) Find the eigenvalues and the corresponding wave functions for the potential well. b) (Ensy) Write the full wave function for the fermions in singlet state with possible minimum energy. e) (Easy) Write the full wave function for the fermions in triplet state with possible minimum energy.
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Transcribed Image Text:### Quantum Mechanics Problem: Infinite-Wall Potential
**Problem 3:**
Consider a one-dimensional infinite-wall potential \( V = \infty \) for \( x > L \) and \( x < 0 \), and \( V = 0 \) for \( 0 \leq x \leq L \).
There are two identical spin half fermions in this potential well and spin states are denoted by \(|\uparrow\rangle\) and \(|\downarrow\rangle\) for spin up and down, respectively.
a) **(Very easy)** Find the eigenvalues and the corresponding wave functions for the potential well.
b) **(Easy)** Write the full wave function for the fermions in singlet state with possible minimum energy.
c) **(Easy)** Write the full wave function for the fermions in triplet state with possible minimum energy.
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