Quantum Mechanics Problem 1 Consider the three spin-1 matrices ⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛=0101010102hxS; ⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−=000002iiiiSyh; ⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−=100000001hzS(a) Calculate the commutator of and . xSyS(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 2Consider a one-dimensional step potential of the form: ⎩⎨⎧=00)(VxV00≥<xxwhere A quantum particle with mass m and energy is incident on this step “from the left” as shown in the figure. .00>V0VE>(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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