Homework Statement
I am tying to prove the following:
\Gamma^{a}_{bc} T^{bc} =0
Homework Equations
The Attempt at a Solution
I approached this problem as follows:
dx_{b}/dx^{c} * e^{a} (e^{b} . e^{c}) but it did not yield anything.
Then I expanded the christoeffel symbols into...
I looked at the stirling formula derivation but I don't know how it is helpful here.
So I have solved it the other way.
[N-(n-(n-0))] [N-(n-(n-1))] [N-(n-(n-2))] [N-(n-(n-3))]......[N-( n-(3) )][N-( n-(2) )][N-( n-(1) )]
For N>>n, using this approximation once, I get n terms:
[N-n] [N-n]...
Homework Statement
The question requires me to approximate binomial distribution to get poisson distribution.
Show that N!/(N-n)!=N^n.
Homework Equations
N!/n!(N-n)! p^n q^(N-n)=Binomial distribution
The Attempt at a Solution
I expanded N!/(N-n)! and got...
Hi,
I read the following in an online source:
In relativistic settings, momentum and energy are equal so the uncertainty principle, for a particle of mass m which is trapped in a box of size L, becomes delta E>= \hbarc/L. If uncertainty exceeds delta E=2mc^2, we get pairs of particles and...
Homework Statement
[S2 total, Sz ∅1]
Homework Equations
S2 total = S2∅1+ 1∅S2+2(Sx∅Sx+Sy∅Sy+ Sz∅Sz)
The Attempt at a Solution
I calculated it in steps:
(1∅Sx 2 +Sx 2∅1) * Sz ∅1
=[S2x, Sz] ∅1 + Sz∅Sx 2
=-h_cut i (SxSy+SySx)∅1 + Sz∅Sx 2
Is it correct way of doing it? I...
Homework Statement
Find the eigenvalues and eigenstates of the spin operator S of an electron in the direction
of a unit vector n; assume that n lies in the xz plane.
Homework Equations
S|m>= h m|m>
The Attempt at a Solution
This question is from Zettili QM and they have...
Homework Statement
What must the ratio of height to radius of a cylinder be so that every axis
is a principal axis (with the CM as the origin)?
Homework Equations
Moment of inertia tensor.
I need I_yy = \sum m *(x^2 + z^2)
The Attempt at a Solution
I calculated I_zz = MR^2 /12...
Homework Statement
Attached is the picture of a dumbbell. I do not understand how the coordinate of M1 is
M2 R/ (M1 + M2)
It is not an assignment question but an example from a book.
Homework Statement
Homework Equations
The Attempt at a Solution
QM--- matrix exponentiation
Homework Statement
\
How do you go about exponentiating a 3*3 matrix? for example if you have
<θ,∅|exp(-i*∅*Ly/h)|l,m>
Homework Equations
I know how to exponentiate a two cross two diagonalized matrix. you just exponentiate the diagonal terms...
Homework Statement
|4 + 2r - r^2| <1
Homework Equations
4 + 2r - r^2 = (r - (1+ √5) ) (r - (1 - √5))
The Attempt at a Solution
I tried to use the roots but no use. How should I proceed?
Homework Statement
write the following in K basis:
A=∫|x><x|dx where the integral limits are from -a to a
Homework Equations
The Attempt at a Solution
I tried solving it by inserting the identity
I=∫|k><k|dk where the integral limits are from -∞ to +∞
but then I do not...