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. StevieTNZ

    Probabilities in Quantum Mechanics

    Hi there, The average expected result for particles with 1/2 probability going through slit 1 and 1/2 probabiltiy going through 2, for a large number of particles (N) is exactly that: 1/2 slit 1, 1/2 slit 2. We send the large number of particles through and find that roughly half go...
  2. S

    Significance of commutators in Quantum mechanics

    Homework Statement why we do use commutation? what is physical difference between commutators and Poisson Brackets? Homework Equations The Attempt at a Solution
  3. J

    Measurement in quantum mechanics problem

    Hi all, In our assignment, we were given this question: [PLAIN]http://img685.imageshack.us/img685/4854/prob213.png I know that for (a), the answer is the first energy eigenstate since the measured energy corresponds to it. I'm not sure about the situation in (b), though. Does...
  4. J

    Probability in quantum mechanics

    Hi all, In my class we were given an assignment from Introduction to Quantum Mechanics by David Griffiths. The question is in Chapter 3, problem 3.34. http://img41.imageshack.us/img41/7899/prob334.png (The system has a harmonic oscillator potential.) Right now I'm stuck with...
  5. C

    What is the meaning of quantum in quantum mechanics?

    There are many n's in QM, and I am confused as to which is which. For example, there are: n called principal quantum number n_r=n-l-1 (anonymous n) n_i in E=({3\over2}+n_x+n_y+n_z) and n=\sum_i n_i n the indices of energy as in E_n and lots more Could anyone kindly help me...
  6. H

    Degeneracy in Quantum Mechanics

    Can anyone explain to me what Degeneracy is properly. I know its something to do with having different eigenvalues on the same energy level or something like that, but have not been able to find a good explanation in any textbooks or anywhere online. And how does something have infinite...
  7. M

    How Does Time Evolution Affect Operator Expectation Values in Quantum Mechanics?

    Homework Statement i know that H |n> = \varepsilon_n |n> H |i> = \varepsilon_i |i> and i want to estimate < n | e^{i H t / \hbar} V(t) e^{-i H t / \hbar} |i> Homework Equations <\psi | \varphi> = \int \psi^*(q) \varphi(q) dq The Attempt at a Solution i don't understand well how the...
  8. I

    Explanation of Multiverse Past in Quantum Mechanics

    Hi- I recently read Brian Greene's Fabric of the Cosmos which led me to think of an interesting concept that I would appreciate further explanation on. On page 456 Greene describes how in the multiverse view, if you traveled back to the past, you would have gone back to a past in a parallel...
  9. P

    Maxwell equations in quantum mechanics

    Maxwell equations are based on the wave nature of electromagnetism so they can't explain why the electron revolving in Bohr's orbit does not emit radiations.So my question is can't the Maxwell equations be modified according to the particle nature(quanta) of electromagnetism
  10. T

    Causality in quantum mechanics

    Can someone please elaborate these lines: "Causality applies only to a system which is left undisturbed. If a system is small, we cannot observe it without producing a serious disturbance and hence we cannot expect to find any causal connexion between the results of our observations. "...
  11. M

    Free particle in quantum mechanics, Dirac formalism

    The problem is very easy, maybe just something about eigenvectors that I'm missing. Go to the first two pages of the 5th chapter of ''Principles of Quantum Mechanics'', by Shankar, 2nd edition. Homework Statement Shankar wants to find the solution for a free particle in Quantum Mechanics...
  12. tom.stoer

    Variational principle in quantum mechanics

    I have a question regarding the variational principle in quantum mechanics. Usually we have a Hamiltonian H and we construct a state |ψ> using some trial states. Then we minimize E = <ψ|H|ψ> and get an upper bound for the ground state energy. In many cases the state |ψ> is then used to...
  13. S

    How do mirrors work in quantum mechanics?

    How do mirrors work in quantum mechanics? Does light get absorbed by the atoms and then emitted at the same frequency? Or is something else going on?
  14. O

    Angular momentum addition in quantum mechanics

    Homework Statement There is a combined system with angular momenta j_{1}=\frac{1}{2}, j_{2}=\frac{3}{2} and j_{3}=1. The Hamiltonian of the composite system depends only on the total angular momentum. What are the states of the combined system? What are the degeneracies of the eigenenergies...
  15. V

    Kenneth miller thinks god exists in quantum mechanics

    I'm almost finished with his book finding darwin's god. In short, I feel like he skirts dangerously close to ID with this notion. Basically, Miller reconciles evolution with God by saying that, while this could be reductionist, it was God that created the conditions that led rise to...
  16. SamRoss

    Role of particle's diameter in Quantum Mechanics

    Does a particle's diameter affect anything in determining its position, momentum, energy, etc.? Does it play any role in Shrodinger's equation?
  17. A

    Rotations in Quantum Mechanics Question

    Homework Statement This is more maths than QM I think, but it's at the beginning of my Quantum Questions. Basically, it's about rotations preserving length: xi is the ith component of a vector, and the length of a vector is determined by the metric ηij according to the equation: l2...
  18. G

    Differential equations in Quantum Mechanics

    Studying a maths degree, going onto final year next year, am planning to do a 3rd year course in quantum mechanics. I just want to ask, how much probability theory and differential equations are there in quantum mechanics? Someone said that ultimately quantum mechanics is about probability...
  19. R

    Direct products in quantum mechanics

    Not every state can be represented by a direct product. Do states that can be written as a direct product have anything special about them? It seems that states that can be written as a direct product lose correlation between between each individual state. More specifically, stronger than...
  20. B

    What stage are we at in Quantum Mechanics?

    I am just wondering what stage are we at in Quantum mechanics relative to Newtonian mechanics? I think we are well sorted with the latter but is ourknowledge nowadays of QM equivalent to the egyptians thinking the sun was god thousands of years ago? Shouldnt we start working on theories...
  21. homology

    How Does Quantum Mechanics Explain Pressure Exerted by a Particle in a Box?

    Homework Statement Suppose you have a particle in a box of length L (a cube). Suppose a particle is in a given state specified by three integers n1,n2,n3. By considering how this state must change when the length of the cube is changed in one direction, show that the force exerted by the...
  22. N

    Motion equation in quantum mechanics?

    Please teach me this: Why the motion equation must be:dA/dt=[H,A] where H-Hamintonian,A-operator of any observation,because with a local flow t(time) of vector X in a manifold we can write the Lie derivative:dA/dt=[X,A].(Where we consider time t as one-parameter group and as local flow of some...
  23. tom.stoer

    Entropy in quantum mechanics and second law of thermodynamics

    Can you please tell me were I am wrong? I define the entropy (as usual) as S[\rho] = -k_B \text{tr}(\rho\ln\rho) The time development of the density operator is \rho(t) = U(t)\rho(0) U^\dagger(t) That means S[\rho(t)] = S[U(t)\rho(0) U^\dagger(t)] = S[\rho(0)] where I used...
  24. Z

    Is modelling REALLY impossible in quantum mechanics?

    I am not a physicist, so please excuse the gaps in my knowledge. I am writing a would-be philosophical essay about models in different fields of research. In most general terms, my task is to consider how modelling can be useful in the pursuit of knowledge in the widest understanding of the...
  25. Z

    Is information ALWAYS conserved in quantum mechanics?

    I have been doing some research on Leonard Susskind and how he claims information is conserved. I don't think if we reverse time we will get back what we started EVERY single time. Thinking that information is conserved really doesn't make sense to me. What do you think? If you agree with me...
  26. C

    What is the role of parity in quantum mechanics?

    I'm unsure about how parity is used or indeed what it actually is in quantum mechanics. If someone could shed some light on this it'd be a great help.
  27. Loren Booda

    Golden ratios in quantum mechanics?

    Do golden ratios appear in quantum mechanics - such as with the standard model, string theory or quantum gravity?
  28. J

    Why in Quantum Mechanics is about energy but no force

    In classical mech, we heard of force, but in quantum there is no force mentioned at all. why? I am rather puzzle by this fact.
  29. G

    What means 'coherence' in quantum mechanics?

    I have nothing to add to the question that opens this post.
  30. N

    Solving an Equality in Quantum Mechanics: Help Needed!

    Homework Statement Hi Please take a look at the following equality found in my book: \left| \mu \right\rangle = \sum\limits_v {\left| v \right\rangle \left\langle {v} \mathrel{\left | {\vphantom {v \mu }} \right. \kern-\nulldelimiterspace} {\mu } \right\rangle } =...
  31. M

    Angular momentum operators in quantum mechanics

    Homework Statement H=(J1^2+J2^2)2A+J3^2/2B where J1,2,3 are the angular momentum operators and A and B are just numbers Homework Equations The Attempt at a Solution I rewrote the Hamiltonian as (J^2-Jz^2)/2A + J3^2/2B and got the eigenvalues to be (h^2L(l+1)-h^2m^2)/2A+h^2m^2/2B...
  32. A

    Eigenstates in quantum mechanics

    Homework Statement 1. Is state \psi_{0,2,1}-\psi_{5,0,1} an eigenstate of L_{x} 2. Is state \psi_{1,3,1}-\psi_{4,2,0} an eigenstate of L^{2} Homework Equations Stationary state of Hamiltonian defined by: [itex]\psi_{n,l,m}[/tex] where the subscripts denote quantum numbers. The...
  33. R

    Negative pressure in quantum mechanics

    hi, which phenomena is known in quantum mechanics to cause a negative pressure? as far as I know, the vacuum energy of the time energy uncertainty has a very low energy density but it should have a positive pressure because it pushes and not pulls, am i right? so which phenomena actually...
  34. K

    Operators in Quantum Mechanics

    Homework Statement Find the operator for position x if the operator for momentum p is taken to be \left(\hbar/2m\right)^{1/2}\left(A + B\right), with \left[A,B\right] = 1 and all other commutators zero. Homework Equations Canonical commutation relation \left [ \hat{ x }, \hat{ p } \right ] =...
  35. tom.stoer

    Exploring Canonical Transformations in Quantum Mechanics

    Hello, suppose one has a classical canonical transformation between two sets of canonical variables such that the new (primed) positions and momenta can be written as functions of the old (unprimed) ones. {\cal K}: x_i \to x_i^\prime(x); \quad p_i \to p_i^\prime(p) Using these relations one...
  36. S

    The Definition of Waves in Quantum Mechanics

    I hear the term Wave used in extreme frequencies whenever Quantum Mechanics is discussed but I am not entirely sure what exactly is a wave. Can a wave be thought as a particle whose position is unspecified with multiple areas where it may impact the surface of another object. Or is a wave a...
  37. P

    Prove that 0=1 in quantum mechanics

    Of course every prove of this type have some mistake. If nobody will see I will post solution! \hat{A}, \hat{B} - linear, hermitian operator which commutator is [\hat{A},\hat{B}]=i\hbar\hat{I} \hat{I} - unit operator Eigen problems of operators are: \hat{A}|\psi \rangle=a|\psi...
  38. B

    How are Magnetic Fields described in Quantum Mechanics?

    Apologies for any vagueness or ignorance here (and lack of citations) but I remember reading that ferromagnetism arises from spin behavior of many electrons. So in a broader sense, are all magnetic fields arising from spin? I am trying to understand how magnetic fields can be viewed at the...
  39. O

    What is Velocity in Quantum Mechanics?

    I want to know what does velocity really mean in quantum mechanics. Since the particle doesn’t have exact position, how can we talk about the velocity and momentum?
  40. P

    Velocity of Particles in Quantum Mechanics: Momentum & Computing Mean Values

    How do we define veliocity of a particle in QM? How it's related to the momentum. Are there any ways to cimpute quickly mean value of veliocity.
  41. N

    Energy in quantum mechanics problems

    I'm confused about choosing the value for energy in quantum mechanics problems such as in scattering, tunneling, boundstates.. problems because this affects later calculations. Given the potential in some regions, how do I decide energy to be negative or positive, or greater/less than the energy...
  42. S

    Box Normalizing in Quantum Mechanics: The Role of Black Body Radiation

    What is box normalizing and why is it important in quantum mechanical problems such as the black body radiation?
  43. M

    Solving Problems in Quantum Mechanics, Stat Mech & Atomic Physics

    Are there any other good books such as LIM series which include solved problems on QM,Stat Mech & atomic physics ?
  44. E

    Exploring Fourier's Transformation & Thermical Radiation in Quantum Mechanics

    I read article http://arxiv.org/abs/quant-ph/0401170 It obtains how Dopler frequency change exponentialy with time for accelerated observer. Then it does Fourier's transformation of this waving and it gets thermical radiation. But, where in quantum mechanics it is supported that we make...
  45. L

    Why do particles travel along smooth paths in quantum mechanics?

    I haven't been studying quantum mechanics for very long, and I've only just started reading about the path integral formulation, so I don't know many of the details yet, but I noticed something peculiar. The path integral formulation is possible because of the similarities of the Schroedinger...
  46. H

    Examples of no gravity in quantum mechanics?

    I seem to be missing the resources that describe how gravity is not found in quantum mechanics. What phenomena in quantum mechanics illustrate that gravity is [thus far] not a part of it? This is not a homework question. I know that gravity is incompatible with what we know about QM. What...
  47. E

    Causality in quantum mechanics and relativity

    According to Heisenberg uncertainty principle, certain events such as double slit and decay of an atom has no causal history, hence a violation of causality, uncaused events. But relativity states faster than light travel violates causality. Since quantum mechanics does not respect...
  48. H

    Use of Fourier Transform in Quantum Mechanics

    Homework Statement The solution of Schrodinger’s equation for a free particle can be written in the form: \psi(x,t) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\phi(k)e^{i(kx-wt)}dk [Q1]: Explain why the function \phi(k) is given by: \phi(k) =...
  49. T

    Confused about Parity Operator & Degeneracy in Quantum Mechanics

    We're working on the parity operator in my second semester quantum mechanics class and there is one point I am confused about, either in the definition of degeneracy or in the parity operator itself. We talked about a theorem whereby the parity operator and the Hamiltonian cannot share...
  50. P

    Boundary conditions for two dimensional problems in Quantum mechanics

    I am stuck at the problems of Boundary conditions for two dimensional problem in QM. iIf we have a two-dimensional domain, along the boundary, we can define two directions, one is tangential, the other is normal, assuming that there is no current flowing in and out along the normal direction...
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