1 - Write the one dimensional, time-independent Schrödinger Wave Equation (SWE). Using the appropriate potential energy functions for the following systems, write the complete time independent SWE for:
(a) a particle confined to a one-dimensional infinite square
(b) a one-dimensional harmonic oscillator,
(c) a particle incident on a step potential, and
(d) a particle incident on a barrier potential of finite width.
2 - Find the normalized wavefunctions and energies for the systems in 1(a). Use these wavefunctions to calculate the probability of locating particle within a given region.
3 - Setup the wavefunctions in the different regions for 1(c) (for E > U and E < U) and 1(d) (for E < U).
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