Wave function in an integral

[Cosmossos]

Hello
I need to calculate <x> (x is the location of neutron) and the state is

and the integral is:

Can I move the x to be near the integral symbol? and how to I multiply the matrices?

And is this true:

Can I move the psi to be near the psi*? And psi*x psi =psi^2=1 right?

thanks

 

[Mentz114]

The first vector under the integration should be a row, not a column as you've drawn it. $\bar{x}$ is a square matrix, so the full product is a scalar.

 

[Entropia]

Hello, thank you for your questions. I can provide some guidance on your inquiries.

Firstly, in order to calculate <x>, you will need to use the wave function (often denoted as ψ) and the position operator (x). The wave function represents the probability amplitude of finding a particle at a specific position, while the position operator tells us where the particle is located. To calculate <x>, you will need to use the integral of ψ*x, where * represents the complex conjugate.

Regarding your question about moving x near the integral symbol, it is important to remember that the position operator x operates on the wave function ψ. So, it is not possible to move x inside the integral symbol. You can, however, move it outside the integral as long as it is still operating on ψ.

As for multiplying matrices, the process would depend on the specific matrices you are using. Generally, you would follow the rules of matrix multiplication, which involves multiplying corresponding elements and then adding them together. If you are unsure, it would be best to consult a mathematics textbook or seek guidance from a mathematics expert.

Moving on to your last question, it is not possible to move ψ near ψ* as they are both operators that act on the wave function. However, it is true that ψ*xψ represents the probability of finding a particle at a specific position, and the square of the wave function, |ψ|^2, represents the probability density of finding the particle at a specific position.

I hope this helps clarify your questions. If you have any further inquiries, please feel free to ask. Good luck with your calculations!