3. A particle moving in one dimension has a first excited state eigenfunction associated with the...

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3. A particle moving in one dimension has a first excited state eigenfunction associated with the energy eigenvalue E₁ given by v₁(x) = x vo(x), where to(r) is the ground state wave function associated with the energy eigenvalue Eo. Given that the potential vanishes at x = 0, a) Determine the ratio b) What is the potential V(x) in which the particle moves? 3. A particle moving in one dimension has a first excited state eigenfunction associated with the energy eigenvalue E₁ given by v₁(x) = x vo(x), where to(r) is the ground state wave function associated with the energy eigenvalue Eo. Given that the potential vanishes at x = 0, a) Determine the ratio b) What is the potential V(x) in which the particle moves?