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...
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...
hi
what is a pure quantum state and a mixed quantum state? I looked up the internet but I did not quite understand. For pure quantum state I have read that they can't be written down as a mixture of other states??? are entangled states pure states?
Homework Statement
In the attachment, I do not understand how we got the second equation in terms of polar coordinates.
Homework Equations
The Attempt at a Solution
I tried doing it by writing z_dot = (......)z and then plugging in r* exp i theta, but to no avail.
Hi I have not taken nay course in Topology. So can someone please explain what it means to say "in the neighborhood of some point bifurcation is topologically same"?
thank you.
Homework Statement
The problem is I am unable to understand the proof. I understand how it is done but I do not know how it is related to the theorem. It is probably because I am unable to understand the notation of matrices, the one involving k.
It is given that
I=δ_ij
= 1 0 0...0...
Homework Statement
consider the following rotation matrix:
0 0 1
1 0 0
0 1 0
Find the axis of rotation.
Homework Equations
The Attempt at a Solution
I know the following:
Ω|1> = |2>
Ω|2> = |3>
Ω|3> = |1>
where Ω is an operator.
It is a cyclic permutation. What do not understand is...
Hi!
Can someone please explain how does the limit in the attachment equals the curvature of a trajectory? I do not understand it. Why is it defined this way?
ζ=dx/dl and it is in the direction of T.
Thank you!
for cos y the critical points are n*pi - 0.5*pi
for cos 2x, the critical points should be n/2 * pi - 0.25*pi
because if I set y=2x = n*pi - 0.5*pi , I get the eq in red for x.
However if I do it graphically, I just get n*pi - 0.25*pi.
The question: why algebraically I am constrained to use...
How would you find the roots of:
b - tan (b) = 0
please do not that i have to plot the graphs of y=b and y=tan b and then i should find the solution. I want to know how to do it the other way.
thank you
Hi
Can someone please explain the answer to the following thread? I tried uncoupling the Hamiltonian but to no avail.
https://www.physicsforums.com/showthread.php?t=602106
Thank you.
Hi
I often see the following in books but I do not understand how they are equal. So can someone please tell me for what conditions does the following equality hold?
(\frac{dy}{dx}) 2 = (d2 y)/(dx2)
Homework Statement
Moving in negative x-axis: E1 = E sin(wt + kx)
Moving in right axis: E2 = Esin(wt-kx-θ) moving to right
write complex representation
The Attempt at a Solution
E1= E Im(exp[i*(wt+kx)])
E2= E Im(exp[i*(wt-kx-θ)])
are these correct or do I have to take into...
Hi
I have attached my attempt of solving the infinite square well for Energy. The value I get is different from that of the book, also in the attachment,
Kindly explain if my answer is correct given the fact that I proceeded step by step and used no tricks.
Thank you.
Can someone please explain to me how do we get the following:
[P(x), L(y)]= i h(cut) P(z)
P(x) is the momentum operator with respect to x
and L(y) is the angular momentum operator with respect to y.
I have also attached the solution. I am stuck at the underlined part. I do not know how...
Hi!
The damped oscillator equation is as follows:
x(t)= A exp(γt/2) cos(ωt)
where ω= √( (w0)^2 + (γ^2)/4 )
I have attached a graph of a damped oscillator.
The question is if I use graph to measure angular frequency, will it be w0 or ω?
It should be w0 because if I put γ=0, I should...
Hi all!
If you are given an operator such that A|1> = √(1/3) |1> +√(2/3) |2>, how do we interpret it?
I do know that 1/3 and 2/3 are probabilities but is this operator application on state one suggesting that this state in state 1 and 2 with probabilities 1/3 and /3 respectively?
Thank you!