Recent content by jasonchiang97

I am unsure of what it means by position wave functions of energy eigenstates. Does it mean Solve for ψn(x) for the definite levels of energy levels?

Yes, for a mass moving in 1D, the Schrödinger equation gives Hψn(x) + Vψn(x) = Eψn(x) H = Hamiltonian So if I solve the equation for a 1D box I would get something like ψn(x) = Asin(kx)+Bsin(kx) Do I then solve for k,A, and B?

Homework Statement Consider a particle which is confined in a one-dimensional box of size L, so that the position space wave function ψ(x) has to vanish at x = 0 and x = L. The energy operator is H = p2/2m + V (x), where the potential is V (x) = 0 for 0 < x < L, and V (x) = ∞ otherwise. Find...

Never mind I figured it out. Thanks for the hint!

sorry, do you mean a circle centered at the origin? if that's what you mean then x2 + y2 = R2where x(t) = Rcos(Ωt) and y(t) = Rsin(Ωt) in polar coordinates then ##\vec {r} = x_0\vec {i} + R\cos (Ωt)\vec {i} + R\sin (Ωt)\vec {j} = x_0\vec{i} + x(t)\vec{i} + y(t)\vec{j}## or is the last step...

Homework Statement The position of a participle in a fixed inertial frame of reference is given by the vector r = i(x0 + Rcos(Ωt)) +j(Rsin(Ωt))where x0, R and Ω are constants. a) Show that the particle moves in a circle with constant speed Homework Equations F = mv2/r The Attempt at a...

Oops I meant to write y(t) = v0tsinα - (1/2)gt2 + y0 where y0 is just h, the height so y(t) = v0tsinα - (1/2)gt2 + h

Homework Statement A cannon that is capable of firing a shell at speed v0 is mounted on a vertical tower of height h that overlooks a level plain below. Show that the elevation angle α at which the cannon must be set to achieve maximum range is given by the expression csc2(α) = 2(1+gh/V02)...

I see. Thanks!

Okay, so I multiply by m to get the potential energy, but I don't understand what you mean by adding a constant. So my first term in my expansion should just be 0 somehow?

Homework Statement Show that the variation of gravity with height can be accounted for approximately by the following potential function V = mgz(1+z/re) in which re is the radius of the Earth. find the force given by the above potential function. Homework Equations V = GM/r The Attempt at a...

Right... so in this case, I can say that λ = b' since it asks me to label the common eigenstates as |a',b'> So for an eigenstate of A to be an eigenstate of B, they must have |a'> on the RHS of the equation Edit: I was confused because I thought it told me to show that A|a'> = a'|a'> = B|b'>...

Should I say that Since A|a'> = B|a'> then A and B must share a common eigenbasis? So the eigenstates of A must be the eigenstates of B? edit: and since they only differ by a constant λ then they must be non-degenerate?

Right, there's no way to deduce λ as I'm not given B. However, I'm not sure what to do next.

right, so λ is the eigenvalues of... B in the eigenstate |a'>? |χ> = B|a'> = λ|a'> Since λ is the eigenvalues of B then...I have to solve for λ?