Yeah just by using the formula for the C_n and taking the bra-ket of the eigenvectors and the initial wavefunction. I've finished the rest of the problem. Thank you!
Seems like the way I was doing it with linear algebra is wrong for complex numbers, just taking the dot product sums and square rooting. Any ways do you have any insight in helping in the part C of finding it how it evolves in time? I know I just need to write out the initial state as a linear...
Ahh yes I realize now, I was trying to normalize then in terms of linear algebra instead of quantum mechanics. It looks like it's actually 1/sqrt(59). Normalizing the rest of the vectors and calculating the probabilities using bra-ket squared gives me ~59.322% ~23.73% ~16.95% which sum up to...
Homework Statement
This problem is from Zetelli 3.21
http://imgur.com/wYTNVwz
http://imgur.com/wYTNVwz
Homework Equations
Just the standard probability via product between the eigenfunction and the wavefunction
The Attempt at a Solution
I've found the eigenvectors for the Hamiltonian...
Homework Statement
Hi this isn't really a question but more so understanding an example that was given to me that I not know how it came to it's conclusion. This is a question pertaining linear transformation for coordinate isomorphism between basis.
https://imgur.com/a/UwuACHomework Equations...
Homework Statement
For the spherical harmonics Umn; Vmn, compute the ones of orders
0,1, 2.
Umn=cos(nθ)sinn(\varphi)Pmn(cos(\varphi))
Vmn=sin(nθ)sinn(\varphi)Pmn(cos(\varphi))
(b) How many non-zero spherical harmonics are there of order k?
Homework Equations
Equations of Umn; Vmn...
Hmmm I looked it over again and I get y'2+2ysin(x)-2(yy''+y'2)
For the first part I get: y'2+2ysinx
Second partial: 2yy'
Then derivative of thatis : 2(yy''+y'2)
Ahh so it's the same as you got ty. Why there is no sin in mathematica solution T.T
Homework Statement
Compute the Euler-Lagrange for:
∫y(y')2+y2sinx dx
Homework Equations
\frac{∂L}{∂y}-\frac{d}{dx} (\frac{∂L}{∂y'})
The Attempt at a Solution
Usual computation by hand gives me y'2+2ysin(x) - 2yy'', but Mathematica says it's -y'2-2yy''. Am I doing something wrong?
My apologizes, it's is actually cos^2(ϕ). Edited
So i would consider using the power reduction to get (1+cos(2ϕ))/2. I can use exponential formula for cos, so now my terms \frac{b}{4}e-2iϕ+ \frac{b}{4}z+\frac{b}{2}+a=0. Not sure where I can go from here to find the poles, I can rearrange to get...
I do understand that there's no problem with it. The thing I'm wondering is whether I'm using the correct methods. Right now I'm simply trying to identify the simple poles by trying to solve the denominator, then trying to use residues to compute the integral.
Homework Statement
Calculate the integral
∫\frac{1}{(a+bcos^2(ϕ))^2}dϕ from 0 to 2π a,b >0
Homework Equations
Residue theorem
Cauchy's integral formula
The Attempt at a Solution
The first thing I did was attempt to find the poles of the integral and use residue theorem to solve the...
Homework Statement
There are two circuits in the XY plane: one is a square (side 0.2 m in
length) centered on the origin. The second is circle or radius r also
centered on the origin. The circle is smaller than fits inside) the square.
By assuming the radius of the circle is small compared...
Homework Statement
I need to find the refractive indexes of the core and cladding of an optical fibre by using the specs found here http://www.photonics.byu.edu/FiberOpticConnectors.parts/images/smf28.pdf Then I'm suppose to calculate the Numerical aperture and compare it with the one listed...
Homework Statement
Is work greater in adiabatic or isothermal process?
A piston with oxygen has a final volume 1/4 the initial. The temperature is also 5 times greater. Determine pressure change, heat released or absorbed, and work done on or by gas.
Homework Equations
the work for adiabatic...