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What is psi function? (newbie)

  1. May 7, 2004 #1
    Newbie being me. I am interested in figuring out whether there are many posible outcomes to a situation or one singular future and I think understanding psi function might help me grasp the subject deeper. My problem is math, but I am willing to try to break it down as much as I can and try to get it. Any explanations, pointers, references would welcome and appreciated.

    Zebbler
     
  2. jcsd
  3. May 7, 2004 #2

    chroot

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    I believe you're talking about a quantum-mechanical wavefunction, usually represented by the greek letter psi.

    The wavefunction is just a function that describes the probability of measuring a particle at any given position in space.

    - Warren
     
  4. May 8, 2004 #3
    What is this probability based on? What kind of factors, lets say, do you need to consider when you need to figure out the probabily of particle A being in one spot or another?
     
  5. May 8, 2004 #4

    jcsd

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    One of the equations that gves the wavefunction is the (one-dimensional time dependent to keep things simplier) Schroedinger equation, which has the form:

    [tex]i\hbar\frac{\partial\Psi}{\partial t} = \frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2} + V\Psi[/tex]

    Psi is the wave function, i is the square root of -1, x is postion, h-bar is the Dirac constant (or the rationailzed Planck constant if you like), t is time, m is mass and V (V(x) if you like) is the potential.

    If you were to make a measuremnt, the proabilty of finding the particle at point x at time t, P(x,t), is given by (if we assume that the wavefunction is normalized):

    [tex]P(x,t) = |\Psi (x,t)|^2[/tex]
     
  6. May 8, 2004 #5
    Can we measure Psi-function in any experiment or it is abstract mathematical model of the smeared objects?
    Why smeared object is local when we measuring?
     
  7. May 8, 2004 #6

    chroot

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    You cannot directly measure the wavefunction; however, the wavefunction contains all the information about a particle. You can use the wavefunction to predict the possible outcomes of any measurement, but you cannot measure the wavefunction itself.

    The wavefunction is a model.

    - Warren
     
  8. May 8, 2004 #7
    Why Psi-function is smeared on whole space but microobject is local when we its measurement?
    Is it good model?
     
  9. May 8, 2004 #8

    chroot

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    According to the model, the particle does not really have a defined position until it is measured. Indeed, repeated measurements do not necessarily find the particle in the same place each time; nor do parallel measurements on many identical systems.

    The model is the best physical model to have ever been devised -- it accurately predicts the results of experiments better than any model ever created, to many, many decimal places.

    - Warren
     
  10. May 8, 2004 #9

    jcsd

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    As Chroot implies, in the Copenhagen interpretation , physical significsance shouldn't be attached to the wavefunction, only the possible outxome of measuremnets it predicts. Tgough of course the Copenhagen interpretation in't the only interpretation and other interpretation DO atach physical significance to the wavefunction, but it's a good rule of thumb.
     
  11. May 8, 2004 #10
    Why the microobject is local when we are measurement its position but Psi-function smeared in infinite space?
    We can think that microobject is local but our device for measurement not ideal. For example the analogy of this situation is foto-picture of moving particle with very long time exposition.
     
    Last edited: May 8, 2004
  12. May 8, 2004 #11

    chroot

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    I believe I already answered the question, cartuz.

    And no, the implications of quantum mechanics have nothing to do with the ability (or inability) of our measuring equipment -- that's a common (and naive) misconception. According to the model, particles simply do not have precisely defined positions until measurements are performed.

    - Warren
     
  13. May 8, 2004 #12
    Your statements jcsd regarded as Copenhagen interpretation. This interpretation is not ideal. There is many question.
    The first. We can to measure the particle in point A in the initial time. Throw very shot time we can to observe the particle in infinite far point B. Than the velocity of particle moving is more then constant C - light velocity.
    The second. In this interpretation is destroy the Conservation Energy Law. Really, the particle with small energy can moving throw barrier with bigger energy.
    The next. We must write all classical laws in therm of amplitude probability or in therm of Psi-functions.
    The next. In this case without measurement does not exist coordinates, momentum, energy and ...
    And there is more else.
    And you are named this is the best description.
    We can think that Statistical Physics with Stochastic Classical gravitational fields, with Newton Laws and with classical probability but not quantum Psi-function is will be better to describe the the microobjects as classical test particles. I'm sorry.
     
  14. May 8, 2004 #13

    chroot

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    Riiiiiight. I don't really care what you *think*. Don't post any personal theories here.

    - Warren
     
  15. May 10, 2004 #14
    The wave function psi is the "solution" to the shrodinger equation: HP=EP
    where H is the hamiltonian operator, P is the psi function, and E is energy. The time independent shrodinger equation shows that for a system, say a particle in a 1 dimensional box, the psi function is a function of sines and cosines. A postulate of QM is that once you know what the psi function is you know everything there is to know about that particular system, but unfortunately, the psi function can only be solved for the hydrogen atom and hydrogen-like atoms. Trying to solve the S. equation for say a He is impossible, as of yet, becuase it boils down to solving a 3 body differential equation which has not yet been solved. As a result wave functions have just been approximated for the He atom and all the rest of the other elements in the periodic table. The wave function can only tell you the probabilty of where to find a particle, it can not give you the exact location of a particle because it is impossible according to the heisenberg uncertainty principle. A strange result of QM shows that for a simple model like the particle in a 1-dimensional box, there is a point where the probability of find a particle is zero. That is the particle is going from point A to point B, but there is a point in between A and B where the probability of finding the particle is zero, which means the particle is going from A to B without going through all the points in between A and B. Spooky Huh?
     
  16. May 11, 2004 #15

    HallsofIvy

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    This is very peculiar. You started out by asking what the Psi function was and suddenly you are telling us that the Copenhagen Interpretation is wrong?

    Were you lying to us about your knowledge of quantum physics orginally or have you just learned the equivalent of several years of graduate study overnight?

    Classical physics, even with statistical physics is NOT sufficient- for one thing it doesn't explain "tunneling" which is the basis for all the transistors built into the computer on which you are reading this. If you don't believe that quantum physics works, you had better turn off your computer now!

    "We can to measure the particle in point A in the initial time. Throw very shot time we can to observe the particle in infinite far point B."

    What makes you say that? Certainly such an experiment has never been done. There is nothing in any form or "interpretation" of quantum physics that suggests such a thing.

    "The second. In this interpretation is destroy the Conservation Energy Law. Really, the particle with small energy can moving throw barrier with bigger energy."

    No, it doesn't. Indeed that is one of the things that PROVES that classical mechanics is not enough. It is experimentally verified that particles "with small energy" CAN move through barrier "with bigger energy"- those transistor things I was talking about before do that all the time. In order to do that using classical mechanics the particle WOULD have to violate conservation of energy. Using quantum mechanics, we can have a psi field that has non-zero portions on both sides of the barrier WITHOUT being in the barrier itself- no violation of conservation of energy!
     
  17. May 11, 2004 #16
     
  18. May 11, 2004 #17

    chroot

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    The interpretation is irrelevant. The physics is the same regardless of what interpretation you choose (Copenhagen, many worlds, etc.). The predictions of experimental outcomes do not depend on the interpretation used. The interpretation is just something fun for philosophers to think about.

    - Warren
     
  19. May 11, 2004 #18

    robphy

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    Quantum Cosmologists think about interpretations as well.

    http://www.hep.upenn.edu/~max/everett.html has a paper of possible interest. It starts off with an informal poll of preferred interpretations. Amusingly, it makes reference to a "shut-up-and-calculate interpretation''.
     
  20. May 12, 2004 #19
    I can see classical World only because all device for the measurement is classical. Where is Quantum World? We can suppose that it is exist. Is it true? Is Quantum World exist really?
    From abstract Quantum Phylosophy which based Quantum axioms is follows many and very strange outcomes:
    1. Quantum teleportation.
    I think it is fantasy only and experimental demonstration of this effect is demonstration of correlation two random process.
    2. Quantum objects is non-local.
    We can to describe this effect as two classical test particles in random background fields. Then correlation between its will be non-zero.
     
  21. May 12, 2004 #20

    ZapperZ

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    You forgot to add one extremely important example of the clearest signature of quantum effects: SUPERCONDUCTIVITY.

    To quote Carver Mead of CalTech in his PNAS paper:

    "Although superconductivity was discovered in 1911, the recognition that superconductors manifest quantum phenomena on a macroscopic scale came too late to play a role in the formulation of quantum mechanics. Through modern experimental methods, however, superconducting structures give us direct access to the quantum nature of matter. The superconducting state is a coherent state formed by the collective interaction of a large fraction of the free electrons in a material. Its properties are dominated by known and controllable interactions within the collective ensemble. The dominant interaction is collective because the properties of each electron depend on the state of the entire ensemble, and it is electromagnetic because it couples to the charges of the electrons. Nowhere in natural phenomena do the basic laws of physics manifest themselves with more crystalline clarity."[1]

    I have always tried to emphasize that some of the most convincing evidence of QM (and SR's) validity does not come from some esoteric phenomena, but rather from condensed matter physics/material sciences.

    Zz.

    [1] C. Mead, PNAS v94, p.6013 (1997) or try here: http://www.pnas.org/cgi/reprint/94/12/6013.pdf
     
    Last edited: May 12, 2004
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