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Why is the position of a particle in the Schrödinger wave equation represented as an exponential periodic wave $$A\exp\left(\frac{(2\pi\iota)(px-Et)}{h}\right)$$ where $p$ is momentum and $E$ is the energy of the particle even if Heisenberg uncertainty principle tells we can't find its position accurately?

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  • $\begingroup$ Hello! Please only ask one question per post – otherwise it might get closed due to lack of focus. You can always edit your question or ask a new one. Thanks! $\endgroup$
    – jng224
    Aug 27, 2021 at 15:39
  • $\begingroup$ For your first question: A wave equation doesn't give you the exact position – you can only find probabilities of possible positions by squaring the wavefunction. $\endgroup$
    – jng224
    Aug 27, 2021 at 15:40
  • $\begingroup$ @Jonas i will keep in mind to ask one question per post. Thank you for the information. $\endgroup$
    – User 1
    Aug 27, 2021 at 15:45
  • $\begingroup$ I have edited the question. $\endgroup$
    – User 1
    Aug 27, 2021 at 15:56
  • $\begingroup$ A is infinite for this state, but if you instead chose it as a Gaussian of enormous arbitrary width and computed ΔxΔp ... $\endgroup$ Aug 27, 2021 at 16:12

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In quantum mechanics, at any instant of time you can associate a function with the system. In the example, you gave $A\exp\left(\frac{(2\pi i)(px-Et)}{h}\right)$ is the function associated with the system at time t where time t should be kept fixed. For example, at t=0, the system is described by the function $ A\exp\left(\frac{(2\pi i)(px)}{h}\right)$. It is not something like a 'displacement' in the position x and time t. This function gives all the information you can achieve from the system as permitted by theory. And remember quantum mechanics does not ask "what is the value of this quantity (e.g velocity, position)?" , rather it asks "what is the probability of getting that value for that quantity (e.g. what is probability of getting the position of the particle in the range [1,3])" and "what is the average value of this quantity(e.g. position) if the experiment to measure the quantity(e.g position) is repeated for a large number of time?" And in most cases quantum mechanics can not predict the outcome of a physical quantity in a particular measurement. However, the questions which QM can indeed answer at least in principle are suplied with the help of this function $\psi$. So, I would say that it does not have a physical interpretation as in the case of "displacement" in the example lf wave. It is more or less a mathematical tool for getting answer.

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  • $\begingroup$ Thank you @Muntafa Mubarrat Mahi. $\endgroup$
    – User 1
    Sep 5, 2021 at 7:44

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