Question

A “wavicel” (wave-particle-duality thingy) is confined to be in a very small but finite region of one dimensional space. (Interpret the confinement as the existence of walls that this thingy is never able to penetrate or overcome, while it is able to move in its allotted region of space freely.)

(a) Calculated the expectation value of position (x) and its spread (Δx) for the first exited state of that thingy.

Calculate now the expectation value for the momentum (p) and its spread (Δp) for the same state.

Calculate the product of the two spreads (Δx Δp) and relate it to Heisenberg's uncertainty principle (Relating means in this context: does your product obey or violate (in both a numerical and conceptual sense) Heisenberg's principle?)

While the thingy remains in this state, will the expectation values of the square of momentum, kinetic energy, and total energy all be sharp?

Answer 1

When we performing integration in order to find the expectation values of an operator always perform the operation of the operator first and then integrate it. Due to the time limit and time-consuming process, I here just tell you the process that how things can help you to solve this problem briefly.

Enjoy!