1. Wherever “h” is used, assume it refers to Planck’s constant: h = 6.626 x 10-34J·s...

1. Wherever “h” is used, assume it refers to Planck’s constant: h = 6.626 x 10-34J·s or 4.136 x 10-15 eV·s.Consider a “particle in a box” (where the “box” is aregion where potential energy U(x) = 0 for 0 < x < L and U = elsewhere. Assume there is zero probability of a particle being found outside the box (where the potential energy function is infinite).

a. Write two boundary conditions for Ψ: one x = 0 and another for x = L:

Ψ(0)=

Ψ(L) =

b. Assume the solutions to the Schrodinger equation take the form of sines or cosines. Use the boundary conditions that you generated in (a) to complete the equation for the wave function(s) for the particle and showthat the solution satisfies the boundary conditions. These solutions are not required to be normalizedwave functions.

Ψn(x)=

c. Write out a mathematical expression(without having to solve it here) that would allow the functions Ψn to be normalized. Note that the normalization constant turns out to be √2?

Expert Solution

The potential energy is zero inside the box and goes to infinity at the wall of the box.

the walls of infinite potential energy to ensure that the particle has zero probability of being at a wall for outside the box.

genius_generous answered 2 years ago

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