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Thread: Physical significance of the wave function

  1. #1 Physical significance of the wave function 
    Forum Masters Degree organic god's Avatar
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    Ok this probably only applies to anyone who has studied some quantum physics so if you haven't, you can read up or just totally ignore my post.

    For those of you who have studied you were probably told that the wave function has no physical significance and that it is the square of the wave function which gives us information about probabilities etc.

    However it is my belief that the wave function can give us very useful information and is not completely useless.

    for example. consider the particle in the box. we have the formula
    wavefunction = A sin (kx)

    now if you were asked to locate a position of maximum probabilty. you would think it would involve squaring the wave function, differentiating this new function. followed by finding the value of x for which. d/dx = 0. then finding the second derivative to locate maxima.

    however if you compare the two curves of sin x and sin^2 (x). it is clear that the maximum probability or the maximum of sin^2 (x), occurs whenever a stationary point is reached on the sin curve minimum or maximum. so to locate maximum probabilities,
    it is simply a case of differentiating the wave function. then finding x values for which d/dx = 0. no need for a second differential either.

    this doesn't give physical information (probabilities) but i think it is easy to dismiss the wave function as having no significance.
    I have decided to make it a side project of mine to investigate the significance of the wave function and give it a fair trial.

    watch this space.


    everything is mathematical.
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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    I'll say upfront that I haven't studied QM, but from what little I do know, I think that the wave equation is rarely (if ever) that simple.


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  4. #3  
    Forum Masters Degree organic god's Avatar
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    the equation i gave is a generic equation for any wave,

    With the particle in a box, the potential energy of the wave is zero everywhere except at the walls where it rises sharply to infinity,

    therefore the wave equation is really that simple in this example, the constants don't really play a part in the point i was trying to make
    everything is mathematical.
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  5. #4 Re: Physical significance of the wave function 
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    Quote Originally Posted by organic god
    Ok this probably only applies to anyone who has studied some quantum physics so if you haven't, you can read up or just totally ignore my post.

    For those of you who have studied you were probably told that the wave function has no physical significance and that it is the square of the wave function which gives us information about probabilities etc.

    However it is my belief that the wave function can give us very useful information and is not completely useless.

    for example. consider the particle in the box. we have the formula
    wavefunction = A sin (kx)

    now if you were asked to locate a position of maximum probabilty. you would think it would involve squaring the wave function, differentiating this new function. followed by finding the value of x for which. d/dx = 0. then finding the second derivative to locate maxima.

    however if you compare the two curves of sin x and sin^2 (x). it is clear that the maximum probability or the maximum of sin^2 (x), occurs whenever a stationary point is reached on the sin curve minimum or maximum. so to locate maximum probabilities,
    it is simply a case of differentiating the wave function. then finding x values for which d/dx = 0. no need for a second differential either.

    this doesn't give physical information (probabilities) but i think it is easy to dismiss the wave function as having no significance.
    I have decided to make it a side project of mine to investigate the significance of the wave function and give it a fair trial.

    watch this space.
    The wave function has immense significance. It describes the quantum state and therefore contains all of the available quantum information.
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  6. #5  
    Forum Masters Degree organic god's Avatar
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    indeed,

    but apparently, physically it tells us very little. but i'm going to investigate to see if this is true
    everything is mathematical.
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  7. #6  
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    Quote Originally Posted by organic god
    indeed,

    but apparently, physically it tells us very little. but i'm going to investigate to see if this is true
    I don't understand. With the application of the appropriate operator (observable) it tells you as much as you are going to find out. So I don't think I understand what you are trying to tell me.

    In any case I look forward to the results of your investigation.
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  8. #7  
    Forum Masters Degree organic god's Avatar
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    hmm i think i actually confused myself on this point and therefore no one really stood a chance of understading what i was saying.

    the wave function does give us lots of information. but it doesn't have a physical significance. like probabilities etc.
    everything is mathematical.
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  9. #8  
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    I am not sure what physcial manifestation you need.

    Look at the communications industry. Look at the Electronics industry.
    These are applications of the wave function.

    There are experiments to show how these waves look like.
    From Sound waves to Light frequency waves.

    The equation from the first post is basic. If you want to see the wave of a certain equation, convert the formula to an electronic circuit and read using an oscilloscope.


    If you need to be more physical, apply resonance principles. This is easier done in lower frequencies since the wavelengths are bigger.
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  10. #9  
    Forum Radioactive Isotope MagiMaster's Avatar
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    I'm pretty sure this is about the wave function of quantum mechanics, and not general waves, which is why I still think that the function posted at the beginning is not particularly applicable.
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  11. #10  
    Forum Masters Degree organic god's Avatar
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    I'm pretty sure this is about the wave function of quantum mechanics, and not general waves, which is why I still think that the function posted at the beginning is not particularly applicable.
    ...look at wave functions for particle in a box then talk. kthnxbye
    everything is mathematical.
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  12. #11  
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    Quote Originally Posted by organic god
    I'm pretty sure this is about the wave function of quantum mechanics, and not general waves, which is why I still think that the function posted at the beginning is not particularly applicable.
    ...look at wave functions for particle in a box then talk. kthnxbye
    I think the definiton that we need is that the wave function, for purposes of this thread, is a solution of the Schrodinger equation with the boundary conditions for whatever specific physical situation you might have in mind.

    Andto organicgod's point, the wave function contains all of the quantum information that is available for the system under consideration. It is the state function. But in order to extract information from it you must do some "processing". So in that sense you do not get information directly from the function and you cannot measure the function directly.

    Inability to directly measure the wave function is one manifestation of the Heisenberg uncertainty principle. You can get information from it, but the application of a measurement operator, or the physical act of taking a measurement changes the wave function. So if you measure position, the wave function is altered and you cannot then measure momentum and believe that you had both position and momentum at the same instant of time -- mathematically the position and momentum operators do not commute.

    The non-commutativity of the position and momentum operators is a reflection of the fact that for an arbitrary function d/dx [xf(x)] is not the same as x[d/dx f(x)]. The operation of differentiation and the operation of multiplication by x do not commute. The Stone VonNeumann Theorem shows that this simple example explains the Heisenberg uncertainty principle in great generality.
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  13. #12  
    Forum Masters Degree organic god's Avatar
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    Inability to directly measure the wave function is one manifestation of the Heisenberg uncertainty principle. You can get information from it, but the application of a measurement operator, or the physical act of taking a measurement changes the wave function. So if you measure position, the wave function is altered and you cannot then measure momentum and believe that you had both position and momentum at the same instant of time -- mathematically the position and momentum operators do not commute.

    The non-commutativity of the position and momentum operators is a reflection of the fact that for an arbitrary function d/dx [xf(x)] is not the same as x[d/dx f(x)]. The operation of differentiation and the operation of multiplication by x do not commute. The Stone VonNeumann Theorem shows that this simple example explains the Heisenberg uncertainty principle in great generality.
    this is a very nice mathematical explanation of the heisenberg principle.

    you can do it analytically which is how i prefer to explain it
    If you know the location of the wave function to within a small region,
    the wave will be 0 everywhere except for a very sharp peak. The only way to obtain this wave would be to superpose many different waves so that the interference pattern creates this sharp peak.
    the debroglie relationship p = h/wavelength shows
    that when we adding waves of different wavelength we are adding waves of different momentum. meaning the momentum is becoming more uncertain.
    As the location tends to a finite value, the number of waves we have to interfere tends to infinity meaning the momentum is completely uncertain
    everything is mathematical.
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