Recent content by squigglywolf

What do you mean <ψ|(1/X^2)|ψ> isn't defined? Maybe my notation is just bad, what I meant by that is expectation value of (1/X^2), where (1/X^2)|x> = (1/x^2)|x> . In general <1/X^2> ≠ 1/<X^2>. But yes I see, so I should be able to get the right result by expanding that bracket, looks tedious...

Yeah I don't mean division, I guess it would be the inverse of X^2? Since <ψ|(X^2)(1/X^2)|ψ> will just be <ψ|ψ>. And yeah I don't just want to be able to work out 1/<X^2> which is easily done, I want <1/X^2>. So how do I find the inverse of X^2 = (h/2mw)[a^2 + aa' + a'a +a'^2] ? I need some...

Is it possible to express ANY observable A(X,P) in terms of the ladder operators? I know how to evaluate expectation values in the |n> basis given the operators in terms of a & a+, but was trying to figure out <1/X^2>. How do you express 1/X^2 in terms of ladder operators? <ψ|(1/X^2)|ψ> can be...

So you started with working out [X,P]: [X,P] = xpψ - pxψ as you said. The first bit xpψ= x χ h/i dψ/dx is correct. But pxψ ≠ h/i x dψ/dx Don't know if that was just a mistake typing up but; pxψ = p(xψ) = h/i x dψ/dx +(h/i)ψ <--- since differentiation of product. In the end where {x...

Ah thanks for the references about propagator, forgot about those. In particular the paragraph after 5.1.13 pretty much confirms what I thought, didn't explain it the best myself. Still can't quite grasp how PI gives a proper propagator, it seems that the endpoints (x,t) are fixed to coincide...

Question about the propagator. Am I right in interpreting it in the equation ψ(x,t) = ∫U(x,t;x',t')ψ(x',t') dx' as the transition amplitudes of |x'> to |x> (where these are the position basis vectors) ? Isn't U(x,t;x',t') in ψ(x,t) = ∫U(x,t;x',t')ψ(x',t') dx' kinda saying that, there is a...

Path Integral Formalism Reading through Shankar atm, up to page 232/233. Reference to pages if interested. http://books.google.co.nz/books?id=2zypV5EbKuIC&printsec=frontcover&source=gbs_vpt_reviews#v=onepage&q=232&f=false(sorry I am too noob at latex to type all the formulas out..) It's...

then look up a table or formula for integrals of gaussians

:D. It's moments like these that make you less prone to error in the future :P, atleast I find.

When you took the derivative of S(x) = ∫sin(3πt^2)dt and plugged x into get sin(3πx^2), that counts as differentiating right? Did you do the same to the denominator? You claimed you started with sin(3πx^2)/4x^3, but shouldn't you start with sin(3πx^2)/12x^2 ?

So what is your question exactly? Cant quite follow.

Draw a free body diagram and use symmetry. Consider the force vectors from charge1 and charge2 one at a time, and add them together as per usual. Note the similarities in the forces exerted on charge3 by charge2 and charge1.

uhh just guessing but by looking at that notation, |p> = |t> should represent a state that will be transmitted 100% of the time, and |p> = |a> represents a state that will be absorbed 100% of the time. So a state |p> =1/sqrt(2)[ |t> + |a> ] should represent a state that's in a superposition of...

Hey cool thanks, fortunately my uni has e-book access to it, looks pretty good too. Will definitely give it a read.

Hi. Was wondering if anyone could recommend some good introductory quantum optics textbooks? I have a good grounding in quantum mechanics, but have never looked at quantum optics. Basically my problem is that I am doing my project work in this field(to start in a couple of months) and have...