A free particle moving in one dimension has wave function

$($x$,$t$)=$A$[$ei$($kx$$t$)$ei$(2$kx$4$t$)]($x$,$t$)=$A$[$ei$($kx$$t$)$ei$(2$kx$4$t$)]$

where kk and are positive real constants.

Part A

At tt $=0$ what are the two smallest positive values of xx for which the probability function $|($x$,$t$)|2|($x$,$t$)|2$ is a maximum?

Express your answers in terms of the variable kk and constant $.$ Enter your answers in ascending order separated by a comma.

Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

x$1$x$1,$ x$2$x$2=$

nothing

SubmitRequest$$Answer

Part B

$$At tt $=2$$/$$2$$/$ what are the two smallest positive values of xx for which the probability function $|($x$,$t$)|2|($x$,$t$)|2$ is a maximum?

Express your answers in terms of the variable kk and constant $.$ Enter your answers in ascending order separated by a comma.

Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

x$1$x$1,$ x$2$x$2=$

nothing

SubmitRequest$$Answer

Part C

Calculate vavvav as the distance the maxima have moved divided by the elapsed time. $$

Express your answer in terms of the variables and kk$.$

Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

vavvav $=$

nothing