Recent content by mcheung4

Let w = (w1, w2, w3) wrt to the body frame of a rigid body, where the body frame is right-handed orthonormal. I have gathered 2 definitions of w from different sources and I am confused at how they connect to one another. One is that the RB rotates about w through its CoM at rate abs(w), the...

suppose a uniform rod of mass M and length L is at an angle B to the x axis, one end of the the rod touching the axis. wish to find moment of inertia about x axis. let the rod touches the axis at x=0. let D=density=M/L, and I will integrate along x axis, that means that at a distance x from the...

ok thanks guys!

so ψ(0) = (ψ1 + ψ2)/√2, ψ(t) = U(t,0)ψ(0) = exp(-iHt/ħ)(ψ1 + ψ2)/√2 = [exp(-iE1t/ħ)ψ1 + exp(-iE2t/ħ)ψ]/√2. then find the probability amplitude of (ψ1 + ψ2)/√2 in this time-varying state by taking the inner product ((ψ1 + ψ2)/√2 , ψ(t)), squared it to find the probability = [1 +...

so ψ(x,0) = (ψ1 + ψ2)/√2, and U(t,0) = exp(-iHt/ħ), then ψ(x,t) = U(t,0)ψ(x,0) = exp(-iHt/ħ)(ψ1 + ψ2)/√2 inner product : ∫ [exp(iHt/ħ)((ψ1)* + (ψ2)*)/√2][(ψ1 + ψ2)/√2] dx = exp(iHt/ħ) is this correct? but i don't know what H is here, is it (E1+E2)/2?

Homework Statement A quantum system has Hamiltonian H with normalised eigenstates ψn and corresponding energies En (n = 1,2,3...). A linear operator Q is defined by its action on these states: Qψ1 = ψ2 Qψ2 = ψ1 Qψn = 0, n>2 Show that Q has eigenvalues 1 and -1 and find the...

I am trying to understand how a gaussian packet varies in time. Suppose we have a Gaussian wave packet that is displaced form the origin by an amount x0 and given initial momentum p0. So the wave function in coordinate space is ψ(x,0) =\frac{√β}{√√\pi}exp(-β2(x-x0)2/2)*exp(ip0x/ħ) where...

Homework Statement A particle is in the ground state of a L-box. At t = 0 the wall at x = L is suddenly moved to 2L. (a) If an energy measurement is made after the wall is moved, what is the probability of measuring the energy to be that of the ground state of the new box? (given solution...

(I am referring to section 3.1 in Burkhardt's "Foundations of Quantum Physics", if you happen to have the book.) In that book it's pointed out that the apparent contradiction between the pdf's of the QM ground state solution to the harmoinc oscillator with its classical conterpart (at the...

OK I get the part that we're only seeking normalizable states, and that we cannot have a state corresponding to some negative energy. thanks for all that. But the bit I really don't understand is that how are we so sure that the ladder method generates all the possible states? why energy can...

I am referring to the section The Harmonic Oscillator in Griffiths's introductino to quantum mechanics (the older edition with the black cover). I understand how it all works, however there is a part that I am not sure about. How do we know when we apply a- or a+ (the ladder operators) to a...

thanks interhacker! the link is very helpful!

hi I'm a math undergraduate and looking for books about fluid dynamics, electromagnetism, classical mechanics and quantum mechanics. introductory to intermediate level. would prefer books with lots of examples and include good amount of graphs and diagrams. thanks!

thanks!

I am a maths undergraduate and looking for a book that covers many applied maths topics, such as electromagnetism, fliud dynamics, Newtonian mechanics etc., about introductory to intermediate level. I know it'd be hard to find one that contains all of them so if u have any suggestion on only 1...