He usually models his exam questions off the homework problems he assigns. If he gave this problem on the exam there wouldn't be any way for me to solve for those roots, which made me think I messed up somewhere. If there were at least one integer solution, that term could be factored out by...
First I picked an arbitrary state ##|ϕ⟩=C_1|φ_1⟩+C_2|φ_2⟩+C_3|φ_3⟩## and went to use equation 1. Realizing my answer was a mess of constants and not getting me closer to a ground state energy, I abandoned that approach and went with equation two.
I proceeded to calculate the following matrix...
I'm assuming it's a classical problem because we haven't done anything relativistic all semester, which leads me to the question of where does m2 enter into the problem? It's at rest, so no initial momentum and no initial kinetic energy, and the particle doesn't exist after the collision, so...
Homework Statement
A particle of mass m1 and momentum p1 collides with a particle of mass m2 at rest. A reaction occurs from which two particles of masses m3 and m4 leave the collision along the angles θ3 and θ4 respectively, measured from the original direction of particle 1. Find the energy Q...
Divide by y2/3 on both sides of the original equation, but then I've got a term in front of the y' and that doesn't seem to get me closer to a solution.
1. y' + y = x y2/32. The problem states we need to solve this ODE by using the method of integrating factors. Every example I found on the internet involving this method was of the form:
y' + Py = Q
Where P and Q are functions of x only. In the problem I was given however, Q is a function of...
Derp. Once I read normalization the lightbulb went off in my head.
b = a(sinθcosφ +isinθsinφ) / (cos + 1)
1 - |b2| = |a2|
|a2| = (cosθ + 1)2 / ((cosθ + 1)2 + (sin2θcos2φ +sin2θsin2φ)
|a2| = (cosθ + 1)2 / (2cosθ + 2)
a = √(cosθ + 1)/2 = cos(θ/2)Thank you for the help!
1. n = sinθcosφ i + sinθsinφ j + cos k
σ = σx i + σy j + σz k , where σi is a Pauli spin matrix
Find the eigen vectors for the operator σ⋅n
2. Determinant of (σ⋅n - λI), where I is the identity matrix, needs to equal zero
(σ⋅n - λI)v = 0, where v is an eigen vector, and 0 is the zero vector...
Awesome, guess I'll start plodding away. And I guess just to make sure, for the second part, all I would need to do is set a = 0, integrate over all space, and confirm it equals 1?
1. Problem: Consider vector field A##\left( \vec r \right) = \frac {\vec n} {(r^2+a^2)}## representing the electric field of a point charge, however, regularized by adding a in the denominator. Here ##\vec n = \frac {\vec r} r##. Calculate the divergence of this vector field. Show that in the...
Homework Statement
So, I got the problem from a friend who told me he copied it down in haste, so it's possible that my confusion stems from a missing variable, but I just want to be certain as my exam is in a few days. So the problem states that there's a +2 helium atom that was accelerated by...