Question

3. Ehrenfest's Theorem states that dA i for an observable A and a time-independent Hamiltonian H. Consider a QM system in 1D with time-independent Hamiltonian H 2 V(x). Use Ehrenfest's Theorem to determine Jlx) and p). What is 듦(z)? 4. A projection operator Pn is defined by where there is no summation Ση implied, and the states n> are a complete set of oth onormal states (a) Show that Pa satisfies 2 (b) Show that Pn acting on an arbitrary state lb) projects the state onto the state |n) with probability (nl) (c) Show that the Hamiltonian H can be expressed as when the [n) are energy eigenstates

Answer 1

The solution is given in the attached image.

Since, V(x) is not given, explicitly value can't be calculated.

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