Consider the particle-in-a-box problem in 1D. A particle with mass m is confined to move freely...

Consider the particle-in-a-box problem in 1D. A particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = L. The potential energy function is given as

(a) Describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions).

(b) Solve the Schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, En.

(d) What is the de Broglie wavelength for the ground state?

(e) Sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). Don’t forget to mark the positions of the walls on the graphs.

(f) In a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? What is the corresponding wavelength?

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genius_generous answered 1 year ago

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