Given a 4x4 non-Hermitian matrix, is there any method I can use to prove the eigenvalues are real, aside from actually computing them?
I'm looking for something like the converse of the statement "M is Hermitian implies M has real eigenvalues".
When can one say that the eigenvalues of a...
Homework Statement
A laser of power P with wavelength \lambda is directed through a lens (focal length f) off the optical axis by a distance d. What is the sideways force on the lens?
Homework Equations
Not sure. The average radiation pressure is I/c, where I is the intensity. But this...
M=0.000000007kg
This mass is very small considering the spheres are 2m apart.
I always try to notice these things for myself. This helps me be surprised when I get a surprising answer! And often, a surprising answer to a sundry question is a wrong answer.
Physics has never perfectly described the physical world. It is a science of approximations. (It is only approximations!). In physics, there are many P=0 events. And in the real world? I don't know, but that sort of question isn't physics at all! It's philosophy.
I won't be able to give you very good advice, but I do know one thing: most graduate schools require undergraduates with a background in, at least, classical mechanics, electromagnetism, thermal and statistical physics, and some quantum mechanics. From the sounds of it, you will not be able to...
Keep in mind that physics and engineering, like all pursuits in life, require a huge amount of unexciting work.
I do not mean to say that physics is boring, but for many courses you are investing in your understanding. It will pay off later.
Consider, for instance, how many hours you needed...
This isn't my homework: I'm doing some physics research and I'm stuck at a simple 2 equations. I want to solve these equations
A \cos(\gamma) \sinh(\theta) = \lambda - B \cosh(\theta)
A \cos(\gamma) \cosh(\theta) = A \sin(\gamma) - B \sinh(\theta)
I'd like to know if there's any way I...
Thanks, that's an easy way to remember where zero point energy comes from!
I guess I need to start taking my grade-school physics with a grain of salt, don't I? :smile:
If \Delta x \Delta p > \frac{\hbar}{2}, what happens at T=0? Since "all motion stops" must we have \Delta x diverge?
Or is the zero-point motion allowed to occur at T=0, and only classical kinetic energy is zero?
Typically, scientists use the standard deviation of a set of measurements to quantify the uncertainty. To give a meaningful uncertainty in practice, however, a scientist should also include device precision and reading error.
If a box on a table is not accelerating vertically, the normal force is the force of the table on the box that cancels the net downward force on the box (excluding N). Otherwise, the box would accelerate vertically, wouldn't it?
I am often surprised at the good reputation of some supposedly unknown schools in specific fields. For instance, Rochester does top-notch classical optics, but perhaps most people would not guess this.
However, if the school is not known in your field, a "brand name" school would be an...
If F is the force of friction and N is the normal force, then F = \mu N , where the constant \mu is the friction coefficient.
Learn to love to read your textbook.
Your understanding of the physics is correct, but perhaps you should check if your spring potential energy term with Y_2 is correct. Energy has units of Newton x meter, and the spring constant has units of Newton per meter.
My research suggests one can define a \mu in the direction of J with a Lande factor
g_J= g_L\frac{J(J+1)-S(S+1)+L(L+1)}{2J(J+1)}+g_S\frac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)}
if one is measuring the total angular momentum, say in a magnetic resonance experiment. But as clem said, \mu_J \neq...
Say I know the total angular momentum of my electron as J. If I write the total magnetic moment as \mu = \gamma J then does \gamma = \gamma_{spin} + \gamma_{orbital} ?
Yes, but does it mean that the Wigner-Seitz cell is constructed in the reciprocal lattice and that is the zone? Or that the Wigner-Seitz cell, constructed in real space, is then transformed to k-space, and that is the zone?
Using L'Hopitals rule I can show that \lim_{n \to \infty} \ln f(n) = 0, where f(n) is the original cosine function. If the limit of the \ln is the \ln of the limit, then I am content. Am I misunderstanding what you mean by "take logarithms"?
Thanks for the idea!
I was having a debate with a friend about how to show the following limit.
\lim_{n \to \infty} \cos( \frac{2 \pi}{2n - 2} )^n = 1
I claim that you can just hand-wavingly say that since cosine of 0 is 1, and 1^infinity is 1, the limit is 1. He claims I need to show this using some sort of...
I am confused about the relation between the Wigner-Seitz cell and the first Brillouin zone.
My teacher explained that to find the Wigner-Seitz cell in real space, one draws lines between the lattice points and connects the perpendicular bisecting planes. This constructs the volume nearer to...
Homework Statement
Demonstrate (qualitatively) that an electron in a linearly polarized EM beam that is driven transversely at \omega will also oscillate longitudinally at 2*\omega (due to the B field, apparently).
Homework Equations
I want to use a phasor form for the fields...
The flashlight is left on indefinitely, and the light is transmitted (100%) out of the box. I should have been clear that there is no absorption or reflection.
Homework Statement
A flashlight is shining into a box. There are no reflections. We know the power of the flashlight in Watts. We know the volume of the box.
Question: How much energy (associated with the EM field) is in the box?
Homework Equations
The Attempt at a Solution...
In the first diagram on http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html" [Broken], the band gap in a semiconductor is shown.
What is the corresponding Fermi momentum? If you plug E_F into the dispersion relation, you get no solution for k_F, right?
I ask because an equation is...
I've found the simplest hopping Hamiltonian for fermions (diagonal in momentum space) has a so-called Fermi sea ground state.
H = -2 t \sum_k \cos(k) f^+_k f_k
(t is some parameter in units of energy).
How do I evaluate the expected value of the spin exchange operator S_x \cdot...
Is it true that \sum_x e^{i(k-k')x} = \delta_{k-k'} , where \delta is the Kronecker delta? I've come across a similar relation for the Dirac Delta (when the sum is an integral). I do not understand why k-k' \neq 0 implies the sum is zero.
Edit: In fact, I'm really confused, since it seems...
Hi,
How does one find the s=0 state for the addition of the spin of 4 (for example) electrons?
More generally, how does one obtain the total spin of 4 electrons?
I understand that for 2 electrons one can read the s=1 and s=0 states from a table of Clebsch-Gordan coefficients.
What if I consider a system in a single energy eigenstate?
If the system is prepared in an energy eigenstate, say E1, then surely a measurement of E1 has probability 1 and not 1/Z * e^-E1/kT ?
Or can I not prepare a system that has a definite energy?
Yes, when the photographic film "measures" the position of the photon it collapses the particle's wavefunction.
There is a nice example of the "dots appearing one at a time" in the book Principles of Quantum Physics by French and Taylor. I do not have the book with me, but the figure is 2-2 (or...
I think so, yes.
From my memory of Feynman's books, he may have been trying to express the fact that most physicists postulate that the wavefunction collapses after measurement. If we assume that it is true, we can derive many of the experimental predictions such as the uncertainty relation...
The wavefunction in one dimension is simply some function f(x) that solves Schroedinger's equation. It is called a "wave" function because the Schroedinger equation is mathematically similar to the so-called Wave Equation (Wikipedia explains).
The probability amplitude is the square of the...
I am not involved in quantum optics, but I am skeptical that there is impossibility in detecting single photons as they pass through slits.
See "Heralded Generation of Ultrafast Single Photons in Pure Quantum States" by Mosley in PRL.
I would just like to correct my \Delta x = 0 assertion:
In order to measure the position of a particle, one needs a probe (say a photon, if we use Compton scattering) of sufficient momentum. As the position measurement becomes more ideal (to the limit where we know exactly the particle's...
"Trivial", in this context, implies that the solution vector to the system has each component zero.
For instance, Ax=b, where A is NxN and x,b are N-vectors has solutions x = inv(A) b and x = 0 when A is invertible, but only x = 0 when A is singular.
So, x = 0 is the trivial solution. It is...
First, do not be quick to assume photons have zero width, because otherwise the uncertainly principle would have \Delta x = 0, which is forbidden.
The collapse of the wavefunction can be imagined by detecting the photon as it passes through one slits. With the detector off, the photon is in a...
If you suppose that the nucleons and electrons only need to solve Maxwell's equations, and not the mathematics of quantum mechanics, you discover that even in the hydrogen atom (an electron-proton bound state) the electrostatic attraction implies that H is fundamentally unstable.
Quantizing...
The uncertainty principle is, in fact, linked to Fourier theory. It is a principle of the Fourier transform of all signals (waves) that the time duration and temporal bandwidth product is limited to:
\Delta t \Delta \nu = 1
Further, the spatial frequency k is propotional to the momentum of...