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Quantum Mechanics Problems

# Quantum Mechanics Problems - Quantum Mechanics Problem 1...

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Quantum Mechanics Problem 1 Consider the three spin-1 matrices = 0 1 0 1 0 1 0 1 0 2 h x S ; = 0 0 0 0 0 2 i i i i S y h ; = 1 0 0 0 0 0 0 0 1 h z S (a) Calculate the commutator of and . x S y S (b) What are the possible values we can get if we measure the spin along the x-axis? (c) Suppose we obtain the largest possible value when we measure the spin along the x-axis. If we now measure the spin along the z-axis, what are the probabilities for the various outcomes? Quantum Mechanics Problem 2 Consider a one-dimensional step potential of the form: = 0 0 ) ( V x V 0 0 < x x where A quantum particle with mass m and energy is incident on this step “from the left” as shown in the figure. . 0 0 > V 0 V E > (a) Write down the appropriate solutions of the time-independent Schrödinger equation for this particle in the x < 0 region and the x > 0 region.

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