What is In quantum mechanics: Definition and 256 Discussions

In quantum physics, a measurement is the testing or manipulation of a physical system in order to yield a numerical result. The predictions that quantum physics makes are in general probabilistic. The mathematical tools for making predictions about what measurement outcomes may occur were developed during the 20th century and make use of linear algebra and functional analysis.
Quantum physics has proven to be an empirical success and to have wide-ranging applicability. However, on a more philosophical level, debates continue about the meaning of the measurement concept.

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  1. S

    Creation and annihilation operator in quantum mechanics?

    What is exactly the creation and annihilation operator in quantum mechanics? What its physical significance?
  2. O

    Traveling and Standing Waves in Quantum Mechanics

    Homework Statement A wave in quantum mechanics is represented by Aei(kx-\omegat). Show that a standing wave looks like 2iAe-i\omegatsin(kx) by subtracting two waves moving in opposite directions. (Hint: make the k negative in one of the waves) Homework Equations As far as I know, the 2...
  3. Loren Booda

    Is anything physically impossible in quantum mechanics?

    Some things are statistically impossible in QM, I believe, but are things there physically impossible?
  4. S

    Problem: properties of Fourier Transforms in Quantum Mechanics

    Homework Statement I am trying to derive a property of the Fourier Transform of the wave function. F[\psi(cx)]=\frac{1}{|c|}\overline{\psi}\left(\frac{p}{c}\right) Homework Equations The Fourier transform of \overline{\psi}(p) is defined as...
  5. B

    Ladder operators in quantum mechanics

    Homework Statement This is problem 2.11 from Griffith's QM textbook under the harmonic oscillator section. Show that the lowering operator cannot generate a state of infinite norm, ie, \int | a_{-} \psi |^2 < \infty Homework Equations This isn't so hard, except that I consistently get the...
  6. S

    Position of a proton in Quantum mechanics.

    Homework Statement Find the maximum accuracy that can be found to a proton's position without changing it's (not-realativistic) kinetic energy by more that 1 keV I think this involves Heisenberg's uncertainty principle \Delta x\Delta p=hbar/2 but I am not sure at all. Now to find the...
  7. K

    What is the Significance of the Overall Phase in Quantum Mechanics?

    Hi everyone. I am now learning the perturbation theory in QM. and I have encountered something that puzzles me. from http://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics ) says, "...Since the overall phase is not determined in quantum mechanics, without loss of...
  8. X

    Momentum in Quantum Mechanics: Defining, Measuring, & Interpreting

    In CM, we have a prescription for measuring momentum. Velocity is defined, and we can measure it, and we can find out the momentum. Now, does quantum mechanics have the same prescription for measuring momentum (for a single free particle at least) ? I mean, for a single free particle, can we...
  9. G

    Spectral theory in quantum mechanics

    Can someone please tell me what the integrand in the below equation mean? 1 = \langle \psi | \psi \rangle = \int_{-\infty}^{\infty} d \langle \psi |E_\lambda \psi \rangle where, E_\lambda is an increasing (and absolutely continuous) function of projection operators such that...
  10. maverick280857

    Rotation Operator/Orthogonal matrices in quantum mechanics

    Homework Statement Write all orthogonal matrices in the form e^{i\phi \frac{\hat{n}\bullet\vec{L}}{\hbar}}. Homework Equations The Attempt at a Solution I couldn't understand the question. An orthogonal matrix R satisfies R^{T}R = RR^{T} = I and rotation matrices in 3 dimensions...
  11. P

    Momentum and De Broglie Wavelength in Quantum Mechanics

    what does the momentum in de broglie wavelength signify? i mean how do u defien it...we can define the expectation in momentum but how do we define momentum for "quantum mechanincal" particles
  12. Ahmed Abdullah

    Is there no cause and effect relationship in quantum mechanics?

    i.e things happen for no cause. Thx
  13. J

    Finding the Correct Solution to an Integral in Quantum Mechanics

    Homework Statement I recently tried to do the following integral: an = ∫√(2/a) sin(n∏x/a) cosh(x) dx x=0 to x=a Homework Equations an = ∫√(2/a) sin(βx) cosh(x) dx β = n∏/a sin(βx) = ½i(eiβx – e-iβx) cosh(x) = ½(ex + e-x) The Attempt at a Solution an = ¼ i √(2/a)∫ (eiβx – e-iβx)...
  14. Y

    Probability Density in Quantum Mechanics

    I am trying to calculate the variance of the position of a particle in a one dimensional box (quantum mechanics). I have a wavefunction, and I know the probablilty density is the integral of (the wavefunction squared) with respect to x. Can you please tell me how this wavefunction could be...
  15. Q

    Differential geometry in quantum mechanics - conserved quantities

    Hi everyone. This is kind of a geometry/quantum mechanics question (hope this is the right place to post this). So, in quantum mechanics we consider operators that reside in an infinite dimensional Hilbert space (to speak rather informally). We even have the cool commutator relation, which is...
  16. V

    Dimension of Hilbert Space in Quantum Mechanics

    We know that the Hilbert space of wavefunctions can be spanned by the |x> basis which is a non-countable set of infinite basis kets. Now consider the case of a particle in a box. We say that the space can be spanned by the energy eigenkets of the hamiltonian (each eigenket corresponds to an...
  17. L

    Lagrangians in Quantum Mechanics

    In classical mechanics the Lagrangian depends only on time, position, and velocity. It is not allowed to depend on any higher order derivatives of position. Does this principle remain true for Lagrangians in non-relativistic quantum mechanics? What about relativistic quantum field theory...
  18. C

    Dimensionality and vectors in quantum mechanics

    i was reading about the mathematical formulation of quantum mechanics and how a system at any given time is described by a vector represented by an infinite number of spatial complex number coordinates. does this infinite-dimensional state space have any physical significance or is it just a...
  19. L

    Derivation of current density in quantum mechanics

    I read some derivations of current density from the quantum equations of motion (like Scrödinger's and Klein-Gordon's). They derive an equation with the same form as continuity equation: div(A)+dB/dt=0 Then they conclude that A=current density and B=density. However there are non-zero...
  20. A

    Why forces are modeled as virtual particles in quantum mechanics?

    Why forces are modeled as virtual particles in quantum mechanics and how virtual particles can transmit force between two real particles?
  21. F

    Verifying Rotational Operator in Quantum Mechanics

    hi all, I have a problem about rotation operator in QM. I must verify that (\hat{U}(R)f)(\textbf{x})=f(R^{-1}\textbf{x}) with: \hat{U}(R) = exp({\frac{-i\varphi\textbf{nL}}{\hbar}}) R rotation on versor n of angle \varphi I don't really know how to start, so please give me an advice!
  22. S

    Is It Uncommon for Freshmen to Take Quantum Mechanics in College?

    How rare is it for a freshman in college to be taking quantum mechanics? I know a crazy freshman who is going to be taking it with me next quarter.
  23. Y

    How is the act of observation defined in quantum mechanics?

    Can anyone explain to me what how is the act of observation defined in quantum mechanics? It is commonly said that the double slit experiment shows that if one simply observes the state of the electron as it passes through the slits, it effects the results. Many forms of observations are...
  24. G

    Are O(3) and SO(3) Both Generators of Angular Momentum in Quantum Mechanics?

    I read that the generator of the O(3) group is the angular momentum L and that the generator of the SU(2) group is spin S. Nevertheless I have some questions. 1. In some books they say that the generator of the SO(3) group is angular momentum L. SO(3) is the group of proper rotations...
  25. F

    Understanding Fourrier Transforms in Quantum Mechanics: Help Needed!

    I am studying Quantummechanics, but I don't see how Fourriertransforms in quantum mechanics work I want to know how I can Fourrier Transform the Hydr. ground state, so the transform of \phi\left(r\right)=\left(\frac{1}{\pi a_{0}^3}\right)^\frac{1}{2} e^\left-(\frac{r}{a_{0}}\right)...
  26. S

    Understanding Bound States in Quantum Mechanics

    I have a question about bound states as they relate to a question on my homework... From what I can see, bound states in quantum mechanics are associated with energies that are discrete, not continuous. I don't really understand why... In my homework problem we are given a set of potential...
  27. R

    Lie groups in quantum mechanics

    Is U(t)=exp(-iH/th) a Lie group? Is it an infinite dimensional Lie group? To what 'family' of Lie groups does it belong? thank you
  28. A

    Operators in quantum mechanics

    I'm a newcomer here... so I introduce myself: I've just completed my BS in physics and joining M.Sc... I've interested to take specialisation in Quantum mechanics and will continue in theoretical physics in the future... I'm facing problems understanding the algebra of operators...
  29. B

    Operators and Complete State Descriptions in Quantum Mechanics

    What for do we need operators in QM. Where is the complete state description of a quantum object?
  30. A

    Malus law in quantum mechanics

    Hi, For example, if I were to send |y> = 1/sqrt{2}( |H> + |V> ) photons into a polarizer with a 45 degre angle from horizontal, would the beam loose intensity? How can I calculate it on my own? EDIT: The picture below illustrate what is happening. I am changing the base from x-y to a...
  31. B

    Central potential in quantum mechanics

    Hi all, I'm new to his forum. I'm having trouble with the following question on central potentials. It's an exercise from (Bransden and Joachain, Introduction to quantum mechanics). Homework Statement Suppose V(r) is a central potential, expand around r=0 as V(r)=r^p(b_0+b_1r+\ldots). When...
  32. F

    Finding Probabilities for Electron Spin in Quantum Mechanics

    The spin of an electron is described by a vector psi = column vector with two entries,psi up and psi down Give the general expressions for the probabilities to find Sz= +or- h/2 in a measurement of S^z where Sz=h/2(1 0) as a matrix ( 0 -1) ii)Give the general...
  33. F

    Can anyone help? in quantum mechanics commutator prove [L^x,L^y] = ihL^z

    can anyone help?? in quantum mechanics commutator prove [L^x,L^y] = ihL^z given :L^x =(y^(pz)^-z^(py)^) :L^y =(z^(px)^-x^(pz)^) :L^z =(x^(py)^-y^(px)^) where ^ is just showing its operator prove comutator [L^x,L^y] = ihL^z I am swamped at every hurdle and can't seem to get my...
  34. J

    Probability in Quantum Mechanics

    I'm a biology student, but I take some interest in physics and have read 2 of Stephen Hawking's divulgation books about modern physics and often stop to read something about it in wikipedia. Wich has revealed to obviously not be enough to understand some characteristics of Quantum Mechanics...
  35. U

    Hermitian Operators in quantum mechanics

    Homework Statement Within the framework of quantum mechanics, show that the following are Hermitian operators: a) p=-i\hbar\bigtriangledown b) L=-i\hbar r\times\bigtriangledown Hint: In Cartesian form L is a linear combination of noncommuting Hermitian operators. Homework Equations...
  36. B

    Understanding Parity in Quantum Mechanics

    As part of an exam paper I've been using to revise with, I came across a question that simply says "What is parity?" Well I know vaguely what it is. Its to do with whether a wave is odd or even right? For example for cos and sin odd parity occurs because sin(-x) = -sin(x) and cos(-x) =...
  37. Y

    The Potential Well In Quantum Mechanics

    My calculations always come out all right, but I still feel that I need help conceptualizing the potential well. 1.What does the width(or length) of the well represent? 2.What does the depth of the well represent? Sincerely appreciative, Yonderboy
  38. J

    Hamiltonian (in Quantum Mechanics)

    The Hamiltonian is given: H=Aâ†â + B(â + â†) where â is annihilation operator and ↠is creation operator, and A and B are constants. How can I get the eigenenergy of this Hamiltonian? The given hint is "Use new operator b = câ + d, b† =c↠+ d (c and d are constants, too) But...
  39. S

    Backward Causation in Quantum Mechanics: A Refreshing Discussion

    http://realityconditions.blogspot.com/2006/09/on-price-and-penrose-on-time-asymmetry_18.html" is a very interesting discussion of a proposal to allow backward causation in quantum mechanics. The basic idea is that the time asymmetry of QM ("collapse of the wave function") violates our...
  40. B

    Finding a General Solution for Eigenfunctions in Quantum Mechanics

    First it asks a few questions about what if it were a classical particle approaching the barrier. Much of this I understand and am OK with. Then we start treating the particle as a quantum thing so its governed by the TI Schrodinger EQ. So, what it wants me to do which I am a bit unsure about...
  41. A

    Finding Momentum and Uncertainty in Quantum Mechanics Problem 1.17

    Problem 1.17 in griffiths gives, at time t = 0, the state psi =A(a^2-x^2) for -a to a, and 0 otherwise. It asks then to find the expected value of momentum p at 0 and also the uncertainty in p. How do I do this? The only way momentum is defined is md<x>/dt, and since the state is only for time...
  42. E

    Modeling the Earth-Sun system in Quantum Mechanics

    Hi, We recently solved the hydrogen atom and one of our homework problems asks us to replace the coloumb potential with a gravitational potential. I have the potential as being V(r) = -\frac{GMm}{r} Where M is the mass of the sun, m the mass of the earth. I have calculated the Bohr radius to...
  43. S

    Masters in Quantum Mechanics: Job Prospects

    CAn anybody guide me about what are the prospectus for jobs if one gets masters in quantume mechanics? pls om namah shivay
  44. T

    Average Occupancy of Lower Energy Level in Quantum Mechanics

    Hi, can anybody help me with this problem? I am currently study quantum mechanics and am confused with the BE staticstics. OK, say there are N Bosons in a system with two energy levels. The lower energy level is 0 and the upper level is E. The question is what is the average occupancy of the...
  45. R

    Exploring Delta Function in Quantum Mechanics and Quantum Field Theory

    As I read in my quantum mechanics book the delta function is sometimes called the sampling function because it samples the value of the function at one point. \int {\delta (x - x')} f(x')dx' = f(x) But then I opened a quantum field book and I found equations like that: \phi (x) =...
  46. S

    Exploring Math in Quantum Mechanics

    What kind of math does QM use (beyond calculus, differential equations and linear algebra)?
  47. C

    Probability in quantum mechanics

    When you calculate the probability of an electron being somewhere, eg in the case of orbitals, is the result in the form eg 1/2 or 50%, 1/4 or 25%, etc? Or is it of some other form? Thanks.
  48. T

    Normalization conditions in quantum mechanics

    I am familiar with the normalization \int\left|\Psi\right|^{2}dx=1 Because we want to normalize the probability to 1. However if a state vector isn't in the x basis and is just a general vector in Hilbert space, we can take the normalization condition to be: <\Psi|\Psi>=1...
  49. Loren Booda

    Observer free choice in quantum mechanics?

    Does quantum mechanics allow an observer free choice of measurement?
  50. J

    Probability Density in Quantum Mechanics

    Consider the wave function corresponding to a free particle in one dimension. Construct the probability density and graph it as a function of position. Is this wavefunction normalizable? Now, I think that the function should be Psi = C1*exp(ikx-iEt). Thus, the probability density should be...
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