# Questions tagged [probability]

For questions about probability, probability theory, probability distributions, expected values and related matters. Purely mathematical questions should be asked on Math.SE.

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190 views

### Question on some basic principles of quantum theory [closed]

I asked a physicist (former head of the physics department in a university) about some of the basics of quantum theory and the double slit experiment. Here is his reply. Are any of these points ...
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### Analytical solution to damped harmonic oscillator - Fokker-Planck equation

In the paper "Numerical solution of two dimensional Fokker-Planck equations" (available at: https://doi.org/10.1016/S0096-3003(97)10161-8), the authors quote an analytical solution to the damped ...
90 views

### QM probability density function without Born's rule, invariant to wave-function phase

The QM probability density as a function of the wave function is given by Born's rule as a postulate. This leads to the probability density being invariant to the phase of the wave function. Suppose ...
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### Justification behind using probability density in kinetic gas theory

Let's consider an ideal gas, of some huge number of particles. The Maxwell-Boltzmann distribution describes the probability of measuring a particle speed in a range of speeds, through integration. ...
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### Richard Dawkins marble statue waving possible?

I found the following statement attributed to Richard Dawkins: "A miracle is something that happens, but which is exceedingly surprising. If a marble statue of the Virgin Mary suddenly waved its ...
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### Probabilities in Quantum Mechanics: Measurement Outcomes or More?

In all treatments of quantum mechanics, the probabilistic nature of the theory enters via the Born rule for the statistical properties of the measurement outcomes of some observable. In short, this ...
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### Due to the probabilistic nature of particles, is it possible for a photon to arrive at a location slightly earlier than the speed of light?

Due to particles not having a specific location in space unless it is observed (i.e. it is a probability wave), would this mean that a photon can appear slightly ahead of where the speed of light ...
133 views

### Probability distribution of the overlap between two random quantum states in an $n$-dimensional Hilbert space? [closed]

Let two pure states $|\Psi\rangle$ and $|\Phi\rangle$ be drawn uniformly and independently from an n-dimensional Hilbert space $\mathbb{H}^n$. (see Note). What is the probability distribution of ...
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### What is difference in Dirac Notation for probability and Probability Density in Quantum Mechanics? [closed]

The Dirac Notation for wave function $$\langle\psi|\psi\rangle= \int_{-\infty}^\infty \psi^{*}\psi \,dx$$ $$\text{Probability} = \int_{-\infty}^\infty \psi^{*}\psi \,dx$$ But most often it is ...
343 views

### Understanding wave function graph

I found this graph from the internet that interprets the graphical representation of wave function.I completely understand the wave function that is depicted by blue line but i really am confused ...
71 views

### Proving the preservation for the norm of a wavefunction

How can we prove the preservation for the norm of the wave-function for a specific hamiltonian (say a spin 1/2 particle) for all times?
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### How does $H^2$ effect on the probability of photon detection?

Lets consider an electromagnetic wave, between two ideal conductive plates. Maxwell's theory predicts appearance of a standing waves(of $\textbf{H}$ and $\textbf{E}$), at that nodes($\textbf{E} = 0$)...
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### How much can a wave function tell us?

We can not predict the future by getting the velocity and position of particles since it’s not possible to get both of these together due to the uncertainty principle. But, according to Hawking’s book ...
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### Bohr's Correspondence Principle and the Born Rule

Bohr's correspondence principle and the Born rule are related right? The correspondence principle states that the behavior of systems described by the theory of quantum mechanics reproduces classical ...
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### Probability of finding a particle in a superposition

In QM, is it possible to ask what the probability of finding a particle in a superposition will be? Once a particle is in a superposition, it is possible to find out the probability that it will be ...
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### What is Wave Function? [duplicate]

Well, what is the meaning of wave function? What does it represent? In Schrodinger's equation, we find the value of Ψ. But what is Ψ exactly? Max Born only gave an explanation of what $Ψ^2$ (the ...
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### Negative probability distribution function for Dirac equation

People say that the probability density function of the continuity equation for the Dirac equation is definite positive. I wanted to see it myself and followed the same path as Bjorken & Drell's ...
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### List of Replica Symmetry results for different models?

Does anyone know of a good source that might have a list of problems or models along with what kind of replica symmetry they are conjectured to have? I am aware of some of the more famous results, e....
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### What parameters determine the probability of virtual photon emission/absorption?

Suppose an electron is producing an electric field by emission of virtual photons and interacting with other particles. What parameters determine the probability that it will emit at least one virtual ...
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### Some quantum-mechanical questions [closed]

I have recently started studying quantum mechanics, and here are some things that are really confusing me. Particle in a box: Supposedly, the square of the magnitude of the normalized wave function ...
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### Method to build a polyhedral die with given probabilities [closed]

Let's define a die as a polyhedron that, if rolled over a perfect horizontal plane, ends up being in a physically stable unambiguous state labelled $n$. The die has $N$ states. Each state $n$ has a ...
501 views

### Is the Born rule indeed wrong?

This is a question about the validity of a preprint, arXiv:quant-ph/0509089, which claims that the "Copenhagen Interpretation of QM is incorrect" (same title, authored by Guang-Liang Li and Victor O.K....
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### Interpretation of the wave function in newtonian spacetime

A Newtonian spacetime is a quintuple $(M, \mathcal{O}, \mathcal{A}, \nabla, t)$ where $(M, \mathcal{O}, \mathcal{A}, \nabla)$ is a 4 dimensional differentiable manifold with a torsion free connection, ...
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### Do different liquids have different distributions of kinetic energy of their particles, and does this influence their vapor pressure significantly?

This is a bit of a cross-over between a physics and a chemistry question. When we say a liquid has temperature $T$ we make a statement about the mean kinetic energy of a particle in that liquid. That ...
158 views

### Relation between the propagator and probability for the infinite well

This may be an easy question, but I am really confused about it. For the infinite square well, the (time-dependent) energy eigenfunctions are (inside the well):\psi_n(x,t) = \sqrt{2/L}\:e^{-iE_nt/\...
103 views

### Measurement of a State Not in the Eigenbasis of the Operator

Suppose I have a two dimensional Hilbert space $\{ |0 \rangle,|1\rangle \}$ with these states being orthonormal. Now suppose I have the Hamiltonian $H=|1\rangle \langle 0|+|0\rangle \langle 1| .$ It ...
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### Is the “probabilistic nature of quantum mechanics” and quantum randomness the same?

Digital Physics are a branch of hypotheses about the fundamental physics of our universe. They basically describe the universe as an analogy to a computer and defend that everything in the universe is ...