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Yes. But you do understand why it is mathematically wrong to use the same summation index, don't you?Alexitron said:So for example,(ψ=c1ψ1 + c2ψ2) when calculating the average position (or any other Item A) of a particle, if we had the same summation index we wouldn't have the terms X_12 and X_21. But when we calculate the energy we don't have these mixed (E_12,E_21) terms but eigenvalues (E_1,E_2) due to orthogonality.
Well, i know how the values of <x> and <E> are calculated and that energy is quantized but the position for example is not , but to be honest i don't understand why the conjugate ψ* has different index. The only thing i can think is that we lose the factors A12 and A21 when calculating <A> (what you said in your previous reply). Is that the reason? And what's the physical meaning of A12 and A21 that energy doesn't have (I know why energy doesn't have them)?kith said:Yes. But you do understand why it is mathematically wrong to use the same summation index, don't you?
Forget about QM for a moment and think purely mathematical. ψ is a complex number which can be written as a sum Ʃnψn, and so is ψ*. If you multiply two sums, you can't use the same index because this doesn't yield any mixed terms.Alexitron said:Well, i know how the values of <x> and <E> are calculated and that energy is quantized but the position for example is not (of course for t≠0), but to be honest i don't understand why the conjugate ψ* has different index.
Actually, there's nothing specific to energy here. ψ can be decomposed in an orthogonal set of eigenvectors to any observable, so <A> = Ʃn|cn|²an is the result for the average value of an arbitrary observable A.Alexitron said:And what's the physical meaning of A12 and A21 that energy doesn't have (I know why energy doesn't have them)?
The concept of average value in superposition question refers to the mathematical calculation of the average value of a physical quantity in a quantum system that is in a state of superposition. This average value is calculated by taking into account the probabilities of each possible outcome and weighting them accordingly.
In quantum mechanics, the concept of superposition states that a quantum system can exist in multiple states simultaneously. The average value in superposition question is a way to measure the expected value of a physical quantity in such a system. It takes into account the probabilities of each possible state and gives a single value that represents the expected outcome.
In quantum computing, the ability to manipulate and control superposition states is crucial for performing complex calculations. The average value in superposition question allows us to measure and predict the outcomes of these calculations, making it an essential tool in the development of quantum algorithms and technologies.
The average value in superposition question is calculated by taking the sum of the products of each possible outcome and its corresponding probability. This is represented mathematically as the integral of the physical quantity over all possible states, weighted by the probability of each state.
The average value in superposition question gives us a single value that represents the expected outcome of a physical quantity in a quantum system. This value can provide insights into the behavior and properties of the system, such as the stability of the superposition state and the likelihood of specific outcomes.