(5 points) 2. Independent subsystems and probability interpretation. Consider the time-dependent Schrödinger equation =

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5 Points 2 Independent Subsystems And Probability Interpretation Consider The Time Dependent Schrodinger Equation 1 (57.14 KiB) Viewed 55 times

(5 points) 2. Independent subsystems and probability interpretation. Consider the time-dependent Schrödinger equation = = ay(t) iħ H (t) ( Әt with a Hamiltonian that describes two non-interacting, independent subsystems: H = H + H2, with (H1, H2] = 0. (a) Demonstrate that its solution can be written as a product wave function y(t) = x1(t) 42(t), where 01/2(t) solve the time-depen- dent Schrödinger equation for the subsystem Hamiltonians H1/2. (b) Why is this result consistent with Born's probability amplitude interpretation of the wave function ? (c) Now study the modified wave equation kö?v/ata = H 4. In the case of non-interacting subsystems, would a similar factorization as in (a) work here as well ? =