I posted this question in the homework page but I got no answers, so will try here.(adsbygoogle = window.adsbygoogle || []).push({});

Given the wave function of a (spinless) particle I need to expres in terms of [itex]\psi(\vec{r})[/itex] the probability for simultaneous measurements of X y P_z to yield :

[tex]x_1 \leq x \leq x_2[/tex]

[tex] p_z \geq 0[/tex]

I got the result:

[tex]\int_{-\infty}^{\infty}dz\int_{-\infty}^{\infty}dy\int_{x_1}^{x_2}dx \int_{-\infty}^{\infty}dp_x\int_{-\infty}^{\infty}dp_y\int_0^{\infty}dp_z <\vec{p}|\vec{r}>\psi(\vec{r})<\psi|\vec{p}> [/tex]

To get this I evaluated the expression [itex]<\psi|P_2P_1|\psi>[/itex] where P_1 and P_2 are the proyectors:

[tex]P_1=\int_{-\infty}^{\infty}dz\int_{-\infty}^{\infty}dy\int_{x_1}^{x_2}dx|x,y,z><x,y,z|[/tex]

[tex]P_2=\int_{-\infty}^{\infty}dp_x\int_{-\infty}^{\infty}dp_y\int_0^{\infty}dp_z|p_x,p_y,p_z><p_x,p_y,p_z|[/tex]

I need to know two things: 1) is my result correct? 2) in case it is correct, is there any other more simple or concrete answer?

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# Calculation of probabilities in QM

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