# 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.

193 questions
Filter by
Sorted by
Tagged with
3k views

### Do we actually need negative probabilities in quantum mechanics?

I was reading this thread and I'm a bit confused. The answer says negative probabilities can account for destructive wave interference and the events cancelling out. But if events just cancel out, ...
599 views

### Must a wavefunction be normalisable for a pdf to exist?

My course notes say, for normalised wave functions $\psi(x,t)$, the function $$\rho(x,t)=|\psi(x,t)|^2=\overline{\psi(x,t)}\psi(x,t)$$ gives the $\color{red}{\text{probability density}}$ for the ...
• 137
70 views

### The probability density function $|Ψ|²$ [duplicate]

Max Born stated that $|Ψ|²$ is the probability density of a particle, given its wave function to be $Ψ$. But why is this? Where does this come from?
1 vote
52 views

### How are Gleason's and Kochen-Specker's theorems related?

If, on the one hand, I were to paraphrase Gleason's theorem, it would loosely state that if one can assign a truth value $p_k$ to each basis vector $\vec{u}_k$ such that $\sum_k p_k = 1$, then that ...
• 1,223
84 views

### Why do we only look at transitions between energy-eigenstates, when perturbing a system with an oscillating interaction?

I have some doubts about the usual explanation of sharply peaked emission / absorption spectra, that one can observe when one looks at quantum mechanical systems, for example the hydrogen atom. In ...
• 6,487
69 views

### If states cannot be written as superposition of eigenkets of observable, then how do we measure an observable for that state?

Usually, if we have a state $|\psi\rangle$, and have to measure an observable $A$, then all we do is expand $|\psi\rangle$ in terms of the eigenvectors of observable A, and then the probability of ...
1 vote
105 views

### Why it is a longstanding challenge to reproduce Born rule in Everettian QM?

I'm reading this Sebens and Carroll's paper on Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics. Where they presented their derivations of the Born rule and ...
• 1,305
1 vote
107 views

### Nature of expectation values and Born's rule and the measurement problem

Suppose we take a normalised quantum mechanical wave function of $\Psi (\mathbf{r} ,t)$. If we expand it in a certain form of spatial functions $\psi_{n} (r)$ which is complete orthonormal. Then we ...
• 121
91 views

### Is the Born rule a red herring in explaining the measurement problem? [closed]

Many explanations of the measurement problem try to derive the Born rule from Schrodinger evolution, for example Many worlds. I have two reasons to think the Born rule isn't fundamentally related to ...
142 views

90 views

• 17
212 views

### 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 ...
• 2,296
63 views

### 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 ...
• 21
1 vote
44 views

### 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 $\vec{\psi}^* \cdot \vec{\psi} = f(x,y,z)$ ...
• 306
54 views

### 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 ...
• 6,487
1 vote
58 views

### 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 ...
• 6,670
99 views

### 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 ...
• 73
267 views

### 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 ...
• 503
101 views

• 1,397
1 vote
106 views

### 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 ($x$, $y$...
• 165
1 vote
28 views

### 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 ...
• 55
1 vote
134 views

• 1,563
263 views

### 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 ...
1 vote
480 views

### 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 ...
142 views

### 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 ...
• 65
50 views

### 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 ...
• 1,021
1 vote
158 views

• 825