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### Where does the Born rule come from? [duplicate]

As far as I've read online, there isn't a good explanation for the Born Rule. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives ...
5k views

### Why does the magnitude squared of the wave function give us the probability density? [duplicate]

My question doesn't go much beyond the title: Why does $$\left | \psi \left ( x,t \right ) \right |^{2}$$ give us the probability density of something appearing at a certain location? I understand ...
326 views

### Why must the probability be the integrated square modulus of the wave function [duplicate]

Quantum mechanics uses the wave function to calculate probabilities by taking the square modulus of the wave function as requirement by Max Born. Why should this (squaring of the wave function) be so, ...
205 views

### Probability in QM: derivation or interpretation? [duplicate]

It is known that coordinates $C_k\in\mathbb{C}$ of the QM-state vectors $|\psi\rangle$ has an interpretation as probability weights $p_k$ in the whole state through the formula like $|C_k|^2=p_k$. We ...
163 views

### Can the Born rule be derived? [duplicate]

$\renewcommand{ket}[1]{|#1\rangle}$ If we have a particle and we know the initial state $|\psi\rangle$ of everything that is relevant, and we know the full Hamiltonian $H$, then we should be able to ...
92 views

### Why is the probability that one state $|i\rangle$ ends up in the state $|f\rangle$ given by $|\langle i|f\rangle|^2$? [duplicate]

I've come across this relation numerous times, textbooks use it as if it is obvious. But I have never come across a proof or an intuitive explanation about why is it true. It would be helpful if ...
101 views

### Where does the postulate of quantum mechanic that possible results are eigenvalues come from? [duplicate]

Where does the idea come from, that possible results of quantum measurement are eigenvalues of the operator corresponding to the observable?
13k views

### Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
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### On a measurement level, is quantum mechanics a deterministic theory or a probability theory?

Quantum mechanics is a non-commutative probability theory. As such, it fundamentally behaves differently from classical probability theories. This manifests itself most pronouncedly in the uncertainty ...
2k views

### How can indeterminacy in quantum mechanics be derived from lack of ability to observe a cause?

I don't get this part of quantum mechanics. I get the part that you can't observe particles and not affect their behavior because you are shooting photons to them while you are observing them, but ...
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### Overlap integral and probability

I have a question regarding how to extract probability from an overlap integral. Specifically, I am calculating the probability of a particle in a bound state in a delta potential $V=-\alpha \delta(x)$...
294 views

### If a quantum state is pure why are its observables still probabilistic?

As I understand it, a pure quantum state is one that can be represented as a ket $\lvert\psi\rangle$ in a Hilbert space, and it contains all the information about the state of the system. As such, we ...
157 views

### Does the Born rule imply $L_2$ Space?

I see no formal proof of the Born rule. Well, the normalizing condition $\int_\infty|\Psi|^2dx=1$ is because of Born rule if I am not wrong. Does this imply that our reality is a $L_2$ space? If ...