# Questions tagged [born-rule]

The Born rule is a rule in Quantum Mechanics that states that the probability density $\rho$ is $|\psi|^2$ where $\psi$ is the probability amplitude.

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### Which experiments confirm that the Born rule is $|\psi|^2$ rather than $|\psi|$?

It seems like some experiments on quantum systems, like the electron $g-2$ measurement, do not rely directly on the Born rule, since they are more so measuring inherent characteristics of the ...
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### I'm trying to understand this paper on Born rule in Many-Worlds Interpretation

https://arxiv.org/abs/1405.7907 In particular I would like to understand this paragraph, right before chapter 6: This route to the Born Rule has a simple physical interpretation. Take the wave ...
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### Does Born's rule guarantee component-wise probabilities? [closed]

Suppose I have the wave function $\vec{\psi} = \begin{bmatrix} \psi_x \\ \psi_y \\ \psi_z \end{bmatrix}$. If I understand Born's rule correctly, the equality $\vec{\psi}^* \cdot \vec{\psi} = f(x,y,z)$ ...
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### Born's Rule for states over supernumbers?

For Quantum-mechanics on a Hilbert-space over the complex numbers, the usual scalar product of two states $\langle \phi | \psi \rangle$ and gives the transition amplitude between the two states. The ...
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### A question of the semantic meaning of the (non-relativistic) propagator

In the Wikipedia article it says "the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time". Let us ...
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### Interpretation of Born Rule In QFT

Can we born rule be used to find probability of a particle to exist in a region in QFT using the formula $\int_a^b \psi(x)\psi^*(x)dx$,where $\psi(x)$ is a fermionic field? If yes, please provide ...
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### Wavefunction Amplitude Intuition

Reading the responses to this question: Contradiction in my understanding of wavefunction in finite potential well it seems people are pretty confident that, e.g., the wavefunction of a particle in a ...
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### What is the distribution for a function of different quantum observables?

Suppose we have a quantum mechanical particle prepared in a pure state $\psi$, and an apparatus that can measure the orbital angular momentum of the particle along a specified orthogonal axis ($x$, $y$...
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### Can I interpret the squaring of the wave function like this? [duplicate]

Born rule states that the probability density of the wave function is equal to the square of the function over the given interval. I thought, "Why squared?". I came up with this: "We ...
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### What does Hartle's derivation of the Born rule actually amount to?

There have been many questions asked here on the topic of whether the Born rule can be derived from the rest of the axioms of quantum mechanics. See, for example, this and links therein. However, I ...
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### Probability current (Integral in all space)

So , when we take the integral in all space of the probability current j (as defined in the first relationship here https://en.wikipedia.org/wiki/Probability_current) in non relativistic quantum ...
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### Wave function and uncertainty principle

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 ...
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### Probability resulting from uncertainty when the measuring device exactly clicks?

Background Let's say I have $2$ set of eigenkets of observables of a system $|x_i \rangle$ and $|p_j \rangle$ (which do not commute). Let's say I have a non-ideal detector in the sense the ...
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### Orthonormality condition in quantum mechanics [closed]

What does the orthonormality condition in quantum mechanics truly signify? Does it have a physical meaning? Or is it just a method of normalization applied in order to find the probabilities?
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### Expectation value and the probability of finding a particle [closed]

I'm trying to understand basic quantum physics, as I understand, the expectation value of some random distribution gives us the outcome that we might expect(highest probability) if the event is done ...
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### What is the meaning of probabilities in quantum mechanics?

In quantum mechanics, probabilities are associated with the detection of a physical event by a macroscopic device, or are events at the microscopic level also probabilistic? For example, the ...
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### Why $\psi(x)$ needs to be square integrable?

The question might be due to some incompleteness. A state vector ket, $|\psi\rangle$ can be expanded in terms of position basis as, $$|\psi\rangle = \int |x\rangle \langle x|\psi\rangle dx$$ Now if I ...
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### What are we measuring in a quantum field when we square the wavefunction?

Suppose we are doing a measurement in a particular quantum field, i.e electron field. Are we looking for the probability of the electron to show up at that spot we are measuring or are we measuring ...
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### What is the probability of measuring $p$ in the momentum space?
I have a wave function $\Psi (x,t)$. According to the Max Born postulate, $\lvert\Psi (x,t)\rvert ^2$ is the probability density. This quantity specifies the probability, per length of the $x$ axis, ...