Hi All,
I am going through notes our lecturer gave us, am having some problems with it
Given the wave function where A, lambda and omega are psoitive real constants and
either (x greater and equal to 0) and (-x less than or equal to 0)
1) Normalise Psi, 2) Determine the expectation values of x and x^2
I can derive to far as Then he changes the integral such that
=
Where did the first termof the last expression come out of?
Thanks
yes, Im more comfortable with that too. Next I have a query wrt integration by parts using reduction formulae
Setting up the formulas I get
Assuming the above is correct, do i proceed to calculate I2, I1 and I0? Im not sure where I put in the limits?
Thanks
No the recurence is for indefinite integrals so you have (check the algebra here please):
(you can express in terms of if you like but there is no need)
and so on for , now apply the limits of integration.
There is another way to evaluate the integral, which is to observe that for some quadratic that:
doing the differentiation will then allow you to find the quadratic and so the required integral.
CB
Hi CB. IM stil not sure how you work out the integral. Here is what I got so far.
I have calcd I0 and I1 and substituted into I2. Assuming the above algebra is corect, what is the next step? I'm thinking that since its a definite integral we can eliminate the C0 therefore the above becomes
Thanks
Following on from last thread, I calculate I2 to be equal to .
Assuming this is correct, what do I do with this value in relation to
My lecture notes goes on to let ??? I dont understand the overall methodology of integration by recursion with definite integrals.
Any help appreciated.
Thanks
CB,
It turns out I was mislead by my notes and with some typos and apologies if I mislead you! :-) I just solved the following
using integration by parts without any recursion. I dont know what the recursion calcs where for. If i find out I will inform you.
Thanks