At a certain point in time a particle of mass $m$ has the corresponding function (function of $x$)

 

$$\psi(x)=\begin{cases}Nx \exp[-bx]~~&\text{for}& x\geq 0 \\ 0 ~~&\text{for}& x<0\end{cases}~~~~~~~~b>0~~ N\text{ is a norm a coefficient}$$

 

What's the probability that during a measurement of the momentum for that point in time the momentum has a value between $-\hbar b$ and $+\hbar b$.

This is an interesting exercise I found in one of the textbooks in the library.

So, by intuition I want to compute $\langle p\rangle$, which is

$$\langle p \rangle =\int_0^\infty\psi^*p\psi dx=-\int_0^\infty\psi^*i\hbar\frac{\partial}{\partial x}\psi dx$$

Plugging in $\psi$ and after some fiddling around I still can't seem to solve this problem. Specifically, I don't know how to explicitly find the probability for the given range of $-\hbar b$ to $+\hbar b$.

Any ideas?

At a certain point in time a particle of mass $m$ has the corresponding function (function of $x$)

$$\psi(x)=\begin{cases}Nx \exp[-bx]~~&\text{for}& x\geq 0 \\ 0 ~~&\text{for}& x<0\end{cases}~~~~~~~~b>0~~ N\text{ is a norm a coefficient}$$

What's the probability that during a measurement of the momentum for that point in time the momentum has a value between $-\hbar b$ and $+\hbar b$.

This is an interesting exercise I found in one of the textbooks in the library.

So, by intuition I want to compute $\langle p\rangle$, which is

$$\langle p \rangle =\int_0^\infty\psi^*p\psi dx=-\int_0^\infty\psi^*i\hbar\frac{\partial}{\partial x}\psi dx$$

Plugging in $\psi$ and after some fiddling around I still can't seem to solve this problem. Specifically, I don't know how to explicitly find the probability for the given range of $-\hbar b$ to $+\hbar b$.

Any ideas?

At a certain point in time a particle of mass m has the corresponding function (function of x)

$\psi(x)=\begin{cases}Nx \exp[-bx]~~&\text{for}& x\geq 0 \\ 0 ~~&\text{for}& x<0\end{cases}$ $~~~~~~~~$$b>0$ $~~$ N is a norm a coefficient.

What's the probability that during a measurement of the momentum for that point in time the momentum has a value between $-\hbar b$ and $+\hbar b$.

This is an interesting exercise I found in one of the textbooks in the library.

So, by intuition I want to compute $\langle p\rangle$, which is

$\langle p \rangle =\int_0^\infty\psi^*p\psi dx=-\int_0^\infty\psi^*i\hbar\frac{\partial}{\partial x}\psi dx$.

Plugging in $\psi$ and after some fiddling around I still can't seem to solve this problem. Specifically, I don't know how to explicitly find the probability for the given range of $-\hbar b$ to $+\hbar b$.

Any ideas?

At a certain point in time a particle of mass $m$ has the corresponding function (function of $x$)

$$\psi(x)=\begin{cases}Nx \exp[-bx]~~&\text{for}& x\geq 0 \\ 0 ~~&\text{for}& x<0\end{cases}~~~~~~~~b>0~~ N\text{ is a norm a coefficient}$$

What's the probability that during a measurement of the momentum for that point in time the momentum has a value between $-\hbar b$ and $+\hbar b$.

This is an interesting exercise I found in one of the textbooks in the library.

So, by intuition I want to compute $\langle p\rangle$, which is

$$\langle p \rangle =\int_0^\infty\psi^*p\psi dx=-\int_0^\infty\psi^*i\hbar\frac{\partial}{\partial x}\psi dx$$

Plugging in $\psi$ and after some fiddling around I still can't seem to solve this problem. Specifically, I don't know how to explicitly find the probability for the given range of $-\hbar b$ to $+\hbar b$.

Any ideas?