3 ms·

An integral part of quantum mechanics is the actual discrete states, ie the eigen values which it probabilistically chooses during a wave function collapse. He

An integral part of quantum mechanics is the actual discrete states, ie the eigen values which it probabilistically chooses during a wave function collapse. Hence it doesn't behave like a wave, also it doesn't behave like a particle, it behaves like a mix of both. That is quantum mechanics and we don't fully understand the maths of it yet, ie when do these waves behave like particles and when do they behave like waves ie when do the wave function collapse?

scotty79 7y ago
What I'm saying is you don't have to see eigen values as something of different nature than the wave function. They represent very condensed wave function. Instead of getting rid of all probability by calculating eigenstates you could get rid of just a part of probability (sort of like by using fuzzy numbers in your calculation instead of real numbers) and get something that is close to eigenstates but still is a wave function. If you track such object in time and space you'll see it still obeys Schrodinger equation. Nobody does that because that won't help you with predicting results of your experiments and it's way more work. But it gives you insight some people crave while others feel it's completely unnecessary.
- username90 7y ago
  > What I'm saying is you don't have to see eigen values as something of different nature than the wave function. They represent very condensed wave function. They do not represent very condensed wave functions, have you taken even a single course in quantum mechanics? You should have learned about the Double slit experiment in high school at least, how do you explain that using only the schrödiner equation? https://en.wikipedia.org/wiki/Double-slit_experiment https://en.wikipedia.org/wiki/Double-slit_experiment
  - kgwgk 7y ago
    Why do you think the result of the double slit experiment cannot be explained using Schroedinger's equation? If there is a problem at the time of the measurement this is not something specific to the double slit, the same problem exists with a single slit and in any detection of any particle ever.
  - scotty79 7y ago
    The wave function are reshaped by the slits. When it interacts with the barrier with two slits it gets reshaped to have for example very low value directly after the barier far away from the slits. And then final reshaping into something extremely sharp occurs at the screen. The final reshaping is so precise that given photon wave function gets condensed precisely to a single atom of a particle of the photographic dye. Anything except for those reshapings is governed by Schrodinger equation. > [Eigenvalues] do not represent very condensed wave functions User kgwgk said: "Note that eigenvalues are wavefunctions just like any other state" Even if mathematically they don't. Same way as limit of a function at some point outside the domain of a fuction is not a value of that function. But if you consider something close to that limit it is still value of that function. Limits are useful for calculations but if the function represents someting real, limits unlike the function don't actually exist. They are one step more removed from reality than the function is. What I'm saying is that it might be useful for developing intuition for quantum mechanics to consider that eigenvalues don't exist. That they are just mathematical constructs that are useful to represent wavefunctions that are close in shape to them. The genral tendency is exactly opposite. To consider wave function to be mathematical construct (becouse complex numbers and no macroscopic analog) and eigenvectors and states they describe as reality (just because we measured something close to their precisely calculated values).
    - kgwgk 7y ago
      The interaction with the slits is governed by Schroedinger’s equation because it is not a measurement (if it is a measurement the interference pattern disappears).
      - scotty79 7y ago
        Sort of. Shrodinger equation doesn't so much describe interaction with the slit barrier as it describes propagation through space not occupied by the slit barrier. The only difference between passing through a slit and the measurement at the screen is the size and location of the "hole". Measurement at the screen is just a silt of the size of single atom. If your measurement is just ensuring that photon passed through one slit not the other you no longer have interference pattern at the screen but you still get diffraction pattern. Your measurement didn't collapse a wave to single point because it wasn't precise enough.
- deleted 7y ago
  [deleted]
- kgwgk 7y ago
  Note that eigenvalues are wavefunctions just like any other state (and obey Schroedinger’s equation just like any other state). The issue is with the process taking you from one state to another, not with the states themselves.

scotty79 7y ago

What I'm saying is you don't have to see eigen values as something of different nature than the wave function. They represent very condensed wave function. Instead of getting rid of all probability by calculating eigenstates you could get rid of just a part of probability (sort of like by using fuzzy numbers in your calculation instead of real numbers) and get something that is close to eigenstates but still is a wave function. If you track such object in time and space you'll see it still obeys Schrodinger equation. Nobody does that because that won't help you with predicting results of your experiments and it's way more work. But it gives you insight some people crave while others feel it's completely unnecessary.

username90 7y ago
> What I'm saying is you don't have to see eigen values as something of different nature than the wave function. They represent very condensed wave function. They do not represent very condensed wave functions, have you taken even a single course in quantum mechanics? You should have learned about the Double slit experiment in high school at least, how do you explain that using only the schrödiner equation? https://en.wikipedia.org/wiki/Double-slit_experiment https://en.wikipedia.org/wiki/Double-slit_experiment
- kgwgk 7y ago
  Why do you think the result of the double slit experiment cannot be explained using Schroedinger's equation? If there is a problem at the time of the measurement this is not something specific to the double slit, the same problem exists with a single slit and in any detection of any particle ever.
- scotty79 7y ago
  The wave function are reshaped by the slits. When it interacts with the barrier with two slits it gets reshaped to have for example very low value directly after the barier far away from the slits. And then final reshaping into something extremely sharp occurs at the screen. The final reshaping is so precise that given photon wave function gets condensed precisely to a single atom of a particle of the photographic dye. Anything except for those reshapings is governed by Schrodinger equation. > [Eigenvalues] do not represent very condensed wave functions User kgwgk said: "Note that eigenvalues are wavefunctions just like any other state" Even if mathematically they don't. Same way as limit of a function at some point outside the domain of a fuction is not a value of that function. But if you consider something close to that limit it is still value of that function. Limits are useful for calculations but if the function represents someting real, limits unlike the function don't actually exist. They are one step more removed from reality than the function is. What I'm saying is that it might be useful for developing intuition for quantum mechanics to consider that eigenvalues don't exist. That they are just mathematical constructs that are useful to represent wavefunctions that are close in shape to them. The genral tendency is exactly opposite. To consider wave function to be mathematical construct (becouse complex numbers and no macroscopic analog) and eigenvectors and states they describe as reality (just because we measured something close to their precisely calculated values).
  - kgwgk 7y ago
    The interaction with the slits is governed by Schroedinger’s equation because it is not a measurement (if it is a measurement the interference pattern disappears).
    - scotty79 7y ago
      Sort of. Shrodinger equation doesn't so much describe interaction with the slit barrier as it describes propagation through space not occupied by the slit barrier. The only difference between passing through a slit and the measurement at the screen is the size and location of the "hole". Measurement at the screen is just a silt of the size of single atom. If your measurement is just ensuring that photon passed through one slit not the other you no longer have interference pattern at the screen but you still get diffraction pattern. Your measurement didn't collapse a wave to single point because it wasn't precise enough.
deleted 7y ago
[deleted]
kgwgk 7y ago
Note that eigenvalues are wavefunctions just like any other state (and obey Schroedinger’s equation just like any other state). The issue is with the process taking you from one state to another, not with the states themselves.