Search results for query: *

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    Prove eigenvalues are real

    OK, I'm not surprised. Thanks anyways.
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    Prove eigenvalues are real

    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...
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    Calculating Sideways Force on Lens from Laser Power

    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...
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    Please give me the formula (Newon's law)

    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.
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    Is Zero Probability Possible?

    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.
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    Schools Theoretical Physics and Graduate School

    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...
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    Please give me the formula (Newon's law)

    You are not yet ready, mathematically, for physics. And I don't mean formulas; I mean your logic and intuition.
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    Physics I am thinking of getting a Msc in geophysics.

    The geophysicists I've spoken to claim that the field is very lucrative. A PhD in geophysics will often work in the energy sector searching for oil.
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    How to approach school?

    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...
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    Engineering Engineering in Undergrad and Physics in Grad school

    Many schools offer programs in Engineering Physics or Engineering Science.
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    Throw whatever you have against these 2 equations

    Of course, thanks. I'll try to find a new constraint.
  12. A

    Throw whatever you have against these 2 equations

    A and B are known parameters. Indeed, I have already tabulated them numerically.
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    Throw whatever you have against these 2 equations

    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...
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    Uncertainty Principle at T=0

    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:
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    Uncertainty Principle at T=0

    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?
  16. A

    The Most Beautiful Equation?

    p = \frac{h}{\lambda}
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    How to work out the uncertainty of some measurements?

    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.
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    Pulley Physics Help: Solve Force to Move Boxes

    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?
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    Schools Is it worth doing a PhD at an unknown University?

    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...
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    Pulley Physics Help: Solve Force to Move Boxes

    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.
  21. A

    Conservation of Energy- spring

    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.
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    Calculating Electron Magnetic Moment: Spin & Orbital Contributions

    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...
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    Calculating Electron Magnetic Moment: Spin & Orbital Contributions

    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} ?
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    Geometric Optics: Mooney Rhomb

    Homework Statement A Mooney rhomb is a quadrilateral prism that converts linear light to circular polarized light. The question is here...
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    Wigner-Seitz = Brillouin Zone?

    Excellent, thanks.
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    Wigner-Seitz = Brillouin Zone?

    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?
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    Limit Theorem: Solving \lim_{n \to \infty} \cos( \frac{2 \pi}{2n - 2} )^n = 1

    Excellent, I understand. Thanks.
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    Limit Theorem: Solving \lim_{n \to \infty} \cos( \frac{2 \pi}{2n - 2} )^n = 1

    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!
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    Limit Theorem: Solving \lim_{n \to \infty} \cos( \frac{2 \pi}{2n - 2} )^n = 1

    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...
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    Wigner-Seitz = Brillouin Zone?

    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...
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    Relativistic-Strength EM Field

    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...
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    Calculating Energy in a Box with a Flashlight

    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.
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    Calculating Energy in a Box with a Flashlight

    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...
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    Single photon and the double slit

    What if you used a beam splitter that divided the laser 50-50 into each slit?
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    Semiconductor Band Gap: Fermi Momentum & Dispersion Relation

    In the first diagram on" [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...
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    Spin Exchange in Fermi Sea - Evaluating S_x \cdot S_{x+1}

    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...
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    Definition of Delta as a Sum

    Thank you both, I've written these handy formulas for my future reference.
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    Definition of Delta as a Sum

    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...
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    Total Angular Momentum of Many Particles

    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.
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    Simple example of the collapse of the wavefunction?

    Yes, you're right. (I realized this in post #8)
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    Boltzmann Factor in QM Language

    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?
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    Simple example of the collapse of the wavefunction?

    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...
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    Simple example of the collapse of the wavefunction?

    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...
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    Probability amplitudes, de Broglie and Schrödinger

    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...
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    Simple example of the collapse of the wavefunction?

    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.
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    Simple example of the collapse of the wavefunction?

    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...
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    Understand the Difference Between Trivial and Non-Trivial Solutions

    "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...
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    Simple example of the collapse of the wavefunction?

    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...
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    Can electrostatic forces explain electron configurations?

    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...
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    Wave-Particle Duality: Photons, Electrons & Heisenberg's Uncertainty

    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...