Fig 311 is a graph of the normalized state function and corr

Fig. 3.1.1 is a graph of the normalized state function and corresponding probability density for a quantum state of a single particle in one dimension at t = 0. The magnitude of the wave function continues to decay smoothly to zero as x righarrow plusminus infinity. Is this function physically admissible? Why or why not? In an ensemble measurement of the position of the panicle in this state, where is the panicle most likely to be found? Is the expectation value of position in this state equal to your answer to (b)? less than your answer? greater than your answer? Explain your reasoning carefully and fully. ) Is the uncertainty in momentum of this state equal to zero? Justify your answer.

Solution

(a) the function is physically admissible, because of probability density which is always less than one.

(b) the particle is most likely to be found at x= 1 position

(c) less than,

(d) uncertainity in momentum is zero, because there is infinite uncertainity in its position.