Operators implementation with operators

[AleksanderPhy]

Hello I may make some mistakes because I am not professional at physics.So I want to know how to
implementate wave function with operators example:p(hat) impletated with ψ so: p(hat)ψ=pψ so as you saw it was momentum operator and momentum operator is:-iħ∂/∂x as you saw it is one diemensional momentum operator.So we have ψ one dimensional so we have ψ(x) and ψ(x)=A sin(kx)+B cos(kx) and we have -iħ∂/∂x A sin(kx)+B cos(kx) is it right and does implement wave function with operator have numeral solution?

 

[blue_leaf77]

p(hat)ψ=pψ

That's only true if $\psi$ is an eigenfunction of the momentum operator, but since in your problem you seem to have assumed that $\psi(x) = A\sin kx + B\cos kx$ which is a superposition of different momentum operator eigenfunctions, your relation "p(hat)ψ=pψ" cannot hold anymore. If what you want is just to operate $i\hbar \partial/\partial x$ on to $\psi(x)$ then just do as the operator told you, that is , partial differentiation.

does implement wave function with operator have numerical solution?

I'm not sure what you meant by "numerical solution". Since it is a function (in position space), you can always calculate its value at any given point $x$.

 

[AleksanderPhy]

Thank you that information helped me a lot.On numerical solution I thoughte like that ψ=3.62 or some other imaginary- and negative- number

 

[blue_leaf77]

On numerical solution I thoughte like that ψ=3.62 or some other imaginary- and negative- number

Your wavefunction is a function of x, to say that $\psi$ has certain value you need to know x (and the other constants). Moreover for real $\psi$ at some point $x$, its value cannot be bigger than one as the wavefunction must be normalized.

 

[AleksanderPhy]

Your information helped me a lot thank you very much(;