Thank you. Clearly I'm just getting confused by new terms and not giving this a proper thought. I should probably take some time to get more familiar with the notation used for statistical mechanics.
First, i'd like to apologize for the vague title. Unfortunately my understanding of the question is equally vague. I think the dXd matrix is meant to be a covariance matrix, so the above equation would be some complex constant multiplied by the covariance matrix. The Tr would referring to the...
I think I have a better understanding now.
If I can show that each r,##\theta##,##\varphi## integral ≠ 0 then the transition should be valid. I know that the radial wave integral will be some non zero value and the ##\varphi## integral would just be 2π so I should be able to compute the...
I believe the integral over r is also important here since the integral is over 3D space. So r ##\theta## and ##\varphi## are all important. I was going into this with the assumption that ψ(r,##\theta##,##\varphi##)=Rnl(r)Ylml(##\theta##,##\varphi##) would be how I describe each states wave...
Homework Statement
One way to establish which transitions are forbidden is to compute the expectation value of the electron’s position vector r using wave functions for both the initial and final states in the transition. That is, compute ∫ΨfrΨidτ where τ represents an integral over all space...
I think I got it.
If I Put the energy operator in terms of momentum then E=P^2/2m then the operator is time independent. Since the integral from -∞ to +∞ = 1 I can take the second derivative of ψ(x) and move the constants outside the integral. This leaves only the constants from the derivative...
Homework Statement
For a region where the potential V=0, the wave function is given by ψ(x)=2αsin(3πx/a). Calculate the energy expectation value of this system. Note that α and a are two different constants.
Homework Equations
ψ(x)=2αsin(3πx/a)
E=K+V=K
K=p^2/2m
∫ψ*Pψdx=Expected momentum...
If you draw a diagram of the motion of the mass you'll see the 15cm distance that the spring was stretched is greater than the distance from the equilibrium position to the fully stretched position. So the given distance x=15cm is greater than xm.
But you do know the distance x=15cm so you may...
Here is what I would do. Just keep in mind that I only have the knowledge of a first year physics student
Particle executes SHM ∴
x(t)=xmcos(ωt-θ)
v(t)=-ωxmsin(ωt-θ)
a(t)=-ω2xmcos(ωt-θ)
F=ma => -1/2kxm2=m(-ω2xm) => ω=√k/m=10rad/s
x̶[̶S̶U̶B̶]̶m̶[̶/̶S̶U̶B̶]̶=̶0̶.̶0̶1̶5̶m̶, ω=10rad/s...
Thank you. I should really search online a bit before giving up...
This makes me believe the .doc file I have is missing information or some information is in the wrong format. I guess it's back to the textbook for the rest of my studying.
yes I know the mass for a proton and an electron. My trouble is knowing for sure if the particle is a proton or electron. Knowing the magnetic field and force vectors should let me determine the velocity vector which would tell me if the particle is a proton or an electron.
I am not sure if I'm...
The mass is determined by whether the particle is a proton or an electron as each of those are known. The only use for the mass is finding the radius of the circle.
The direction of motion of the particle is determined by it's charge in the case of it being either a proton or an electron. A...
So you want to find the equation of motion? Don't forget that the mechanical energy is being affected by gravity as well as the spring. So PEgravity=mgx
You only used the kinetic energy and spring potential energy.
Homework Statement
A particle moves along a circle in a region of uniform magnetic field of magnitude B=4.0 mT. The
particle is either a proton or an electron. It experiences a magnetic force of magnitude 3.2x1015 N.
What are (a) the charge of the particle? (b) The particle speed? (c) The...