Quantum Mechanics: How Do I Find Expectation Values for Position and Momentum?

[itsaakanksha]

Expectation value problem pleasezzz help ASAP

Hi Everyone,

I have a problem on one of my problems in the quantum course.

I need tofind the expectation values <x>,<x^2>, <p> & <p^2> for the function

e^(-(x-xo)^2/2k^2)

please email me if you need theformulaes..

i have them but i get stuck up doing the integration.

letme know
thanks,

Aakanksha Panjwani

ITS URGENT

 

[Gokul43201]

Aakanksha, show us where you are stuck. Also, you have not mentioned what the bounds are : are they +infty to -infty ?

 

[R0man]

Hi Aakanksha,

I understand your urgency to solve this expectation value problem. An expectation value problem in quantum mechanics deals with finding the average value of a physical quantity, such as position or momentum, in a given state. In your case, you are looking for the expectation values of position and momentum for the given function.

To solve this problem, you will need to use the formula for calculating expectation values: <A> = integral of A(x) * |ψ(x)|^2 dx, where A(x) is the physical quantity and ψ(x) is the wave function.

For <x>, you will need to use the formula A(x) = x and ψ(x) = e^(-(x-xo)^2/2k^2). This will give you the integral of xe^(-(x-xo)^2/2k^2) dx, which can be solved using methods of integration such as substitution or integration by parts.

Similarly, for <x^2>, you will need to use the formula A(x) = x^2 and for <p> and <p^2>, you will need to use the momentum operator, A(x) = -iħ(d/dx) and A(x) = (-iħ)^2(d^2/dx^2), respectively.

I hope this helps you solve the problem. If you are still stuck, I suggest reaching out to your professor or classmates for assistance. Good luck!