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1. A particle of mass is confined in a potential given by () =
4 where is a
positive constant. Use the variational method with a trial wave function given
by () = 2 where is a
normalization constant and is a
real, positive parameter to estimate the ground-state energy for this system.
Show all math for full credit.

2. A particle of mass is confined in a one-dimensional box of length with a potential () = 2 for 0 < < and() = everywhere else. Use perturbation theory to the particle-in-a-box wave function solution to find the first-order energy correction to (a) the ground-state energy and (b) the first excited-state energy.1. A particle of mass is confined in a potential given by () = 4 where is a positive constant. Use the variational method with a trial wave function given by () = 2 where is a normalization constant and is a real, positive parameter to estimate the ground-state energy for this system. Show all math for full credit. 2. A particle of mass is confined in a one-dimensional box of length with a potential () = 2 for 0 < < and() = everywhere else. Use perturbation theory to the particle-in-a-box wave function solution to find the first-order energy correction to (a) the ground-state energy and (b) the first excited-state energy.

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