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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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In the pilot-wave theory, is the quantum potential moving electrons randomly inside atoms?

As we know, in the pilot-wave theory (Bohmian mechanics), particles are guided on certain trajectories by the wavefunction. Here (In Bohmian mechanics, do electrons move inside an atom?) I asked about ...
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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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Does the electron act as point charge in scattering theory?

We know that an electron behaves like a point charge, and the probability density of its position is given by the Born rule. Now suppose that we shoot an electron toward an atom, so the electron gets ...
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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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Does the Central Limit Theorem hold for position measurements?

A friend asked me recently if the Central Limit Theorem holds for quantum systems: i.e., if the distribution of measurements (e.g., of position) for any wavefunction would prove approximately normal, ...
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How to understand the kernel as a transition amplitude?

Consider the time evolution operator $U(t_f, t_i)$ that controls the evolution of a wave function according to $|\psi(t_f \rangle = U(t_f, t_i) | \psi(t_i) \rangle$. As I understand it, the Born ...
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How to evaluate the probability when a particle is detected?

Everyone knows the standard probability interpretation of the quantum mechanics. For example, the wave function of some particle at some time $t$ is $\psi (x,t)$. Therefore, if the particle is ...
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Dependence of wave function with time, especially probability density function. And Continuity equation

I was learning Basic Quantum mechanics. I cam across the fluid equation in QM, which suggests $\Psi^*\Psi$ is probability density function. Consider the two statements below Probability will change ...
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Does the wavefunction probabilities have to sum to 1? [duplicate]

In quantum mechanics we are often told that $\int |\psi(x,t)|^2 dx^3 =1$. i.e. the probabilities have to sum to 1. And that this implies the time evolution operator is unitary. But can't we define ...
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Normalisation of quantum states: why?

We all learn that quantum states need to be normalized, as they are associated to probabilities which needs to sum up to one. However, I would like to know whether you have other valid reasons to ...
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Intuitive understanding of a wave function

Looks like wave function is an abstract mathematical object. I was trying to see if there is a simple way to visualize this. Can someone please help with that? I was thinking may be we can think that ...
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Small psi in the time-independent Schrödinger equation

I'm a total beginner in quantum mechanics, and I am learning about time-independent Schrödinger equation. we separate the wave function into two functions $$\Psi(x, t) = \psi(x)\phi(t).$$ Does the ...
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Probability of finding a particle in space [closed]

Given a particle whose wave function is square integrable, what is the probability of finding that particle somewhere in space?
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Can the many worlds interpretation use the Born rule for decoherence? [closed]

If the Many-Worlds Interpretation cannot derive the Born rule does it need mind body dualism to make sense of probabilities? I asked a different question here regarding MWI and circularity. But here'...
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Is there an official list of the postulates of quantum mechanics?

Having been looking at lecture notes, online sources and books, the list of postulates of quantum mechanics seems to vary. For instance, some sources (my lecture notes, for instance) refer to $|\...
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Is the energy of a vibrating string the classical analog to Born's rule?

Consider this Phys.SE question which spells out the energy of a vibrating string as a variant of Hooke's law, and thereby explains why it's proportional to the square of the amplitude (here: the ...
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Two Time Correlation function calculated from Born rule

Update Below I'm having a hard time reconciling two different calculations of the quantum two time correlation function. Consider quantum operator $A$ with eigenvectors $\{|\phi_i\rangle\}$ and ...
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Generalizing Born rule

In Quantum mechanics, The born rule is that the probability is given by $\mid \langle\Phi\mid\Psi\rangle\mid^2$ I understand that this is essential in order that the QM reduces to the correct ...
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A textbook's reading of the Born Interpretation

A textbook states the following: $P(x, t) \ dx $ is the probability that a measurement of the position of the particle described by $\Psi (x, t)$, at time $ t$, will find it in the region $(x, x +...
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I've read that $\langle a | b\rangle$ is a probability amplitude but $\langle a | a\rangle$ is a probability. Why the inconsistency?

I'm studying elementary quantum mechanics, and I've read that $\langle a \vert b \rangle$ is the probability amplitude of a transition from state $a$ to state $b$. Thus, $|\langle a | b \rangle|^2$ ...
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Does a wave function never reach zero probability density?

$$ψ=e^{iκx}$$ Since the wave function is an exponential equation, is there no point with zero probability density of finding a given particle? Does that justify quantum tunneling?
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Finding amplitude of probability

The mathematical structure of quantum mechanics, follows almost inevitably from the concept of a probability amplitude. For James Binney and David Skinner: "With every value in the spectrum of a ...
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What is the physical basis of Born's interpretations?

Did anyone has any idea how Born came up with the probabilistic interpretation of quantum mechanics. It is by all means very bizarre. And then it leads to the idea of copenhagen interpretation. Also ...
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Probability of finding an energy state of a non-normalisable wave-function

Suppose, say, I have the following wave function It represents the wave function of a free particle. I would want to calculate the probability of finding the particle with energy ħk and energy 2ħk. ...
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Probability measure implies quantum mechanics?

The article "Quantum Logic and Probability Theory," by Wilce, has the following in section 1.4: 1.4 The Reconstruction of QM From the single premise that the “experimental propositions” ...
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Does Gleason's Theorem Imply Born's Rule?

Suppose that I accept that there is wave function collapse in quantum mechanics, and that the probabilities associated with each orthogonal subspace are a function of the wave function $\psi$ before ...
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Loschmidt's paradox in Bohmian Mechanics

In Bohmian mechanics, the position of the particles must have a random distribution given by $\rho = |\Psi|^2$, where $\Psi$ is the wave function, in order to be compatible with Born rule in standard ...
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Reconstruct quantum state from probabilities

Given a quantum state, the Born rule lets us compute probabilities. Conversely, given probabilities, can we reconstruct the quantum state? I think the answer is almost trivially positive but how ...
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Born rule and expectation value integral for $L = x \times p$

Physical interpretation of the wave function $\psi (x,t)$ is a probability amplitude for location $x$ and the Fourier transform of $\psi (x,t)$ can be interpreted as a probability amplitude for ...
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Can the complex square of the wave function be interpreted as shape of the particle? [closed]

We know that for wave function of a photon or an electron, the complex square of the wave function is understood as the probability density of finding point like particle in the location. Can anyone ...
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Validity of Born Rule [closed]

The Born rule has been very successful in quantum mechanics. However, the interesting fact about this rule is that it only allows pairwise interference. In other words, there are no interference terms ...
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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 ...
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Implication of Born's rule on the superposition principle

BACKGROUND Born's rule quantifies the interference pattern of a single quantum particle going through two possibles paths A and B as $P = |A|^2 + |B|^2 + ⟨A|B⟩ + ⟨B|A⟩$. The standard interpretation ...
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If the Many Worlds interpretation (MWI) cannot derive the Born rule, would that mean that it is wrong?

All attempts at deriving the born rule in MWI have been shown to be circular in some way. So if it turns out that MWI cannot derive the born rule without some form of circularity, does that mean that ...
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Are there any derivations of the born rule from MWI that work?

Are there any derivations of the born rule from MWI that are not circular and are mathematically consistent? I ask this because Florin Moldoveanu insists that such a derivation from MWI doesn't exist. ...
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What is the initial and rigorous definition of state function $\psi$ in quantum mechanics?

Is the $$ P_{a\le x\le b} (t) = \int\limits_a^b d x\,|\psi(x)|^2 \, $$ and $$ P_{a\le p\le b} (t) = \int\limits_a^b d p\,|\psi(p)|^2 \, $$ results or axiomatic definitions? Sorry if the ...
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What precisely is the wave function a probability density of?

In QM the norm of the wave function $\psi(\vec{x})$ is said to be the probability density that the particle is at $\psi(\vec{x})$ if one would observe its position. Generally, nothing more is ...
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Defining Quantum Mechanics

Does Schrödinger's Equation (Operator form) $[\hat{X},\hat{P}]=i$ Born Rules define Quantum Mechanics?
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Understanding the Mathematical Formalisms of Everetts MWI

Link to article: http://jamesowenweatherall.com/SCPPRG/EverettHugh1957PhDThesis_BarrettComments.pdf I'm writing an essay on Everettian MWI and its incompatibility with Born Rule probabilities. I ...
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Basic question about wave funtions: using the Born rule

I have a textbook giving an example of what the probability is of observing system $Ψ = a|A⟩ + b|B⟩$ in states $a|A⟩$ and $b|B⟩$. I'm not sure I understand it fully. How do I use the Born rule to know ...
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Clashing definition of rays in Weinberg and Sakurai and Born interpretation without normalizability [duplicate]

In Sakurai's Modern Quantum Mechanics, it is stated that One of the physics postulates is that $|\alpha\rangle$ and $c|\alpha\rangle$, with $c\neq 0$, represent the same physical state. In other ...
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Algebra behind the wave function properties [closed]

In lecture, for the tunnelling wave function $$ \psi(x) = C_1\cosh(x/l)+C_2\sinh(x/l)$$ the current density is $$ J = h/(2mi) [ \psi^*(\Delta\psi) - (\Delta\psi)^*\psi] $$ Here is my problem, ...
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Physical interpretation of nodes in quantum mechanics

In Schrödinger's approach to quantum mechanics, we talk about the probability of finding a particle in a definite location in space. Now if we look at a simple quantum mechanical system, say the ...
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Is the wave function the Radon-Nikodym derivative of a complex measure?

I read somewhere (latest version of a webcomic to be honest) that "superposition" means: a complex linear combination of a $0$ state and a $1$ state... Quantum mechanics is just a certain ...
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Probability of a particle that is in a particular position

When I try to find probability of a particle I just take the product of the complex conjugate of the wavefunction and wavefunction itself, and find the integral from $- \infty$ to $\infty$ or any ...
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Born's interpretation of psi

According to the Born's postulates, psi should be atleast differentiable to the first order then why does we not require psi in this case to be differentiable at X = a and X = 0.Also psi comes out to ...
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Why to take the absolute value of the wave function before squaring it?

For obtaining the probability distribution we should take the absolute value of the Schrodingër Wave Function 'Ψ'and then square it. But why to take first the absolute value if the square is going to ...
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Probability of quantum transition

I have a question about a task: We have a particle, which is in a linear combination of the first two states of the harmonic oscillator, which we can parametrise as $|\psi\rangle=\cos(\frac{\...
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What are some experimental verifications of Born's rule in quantum mechanics?

Born's rule in quantum mechanics states that when measuring a system using a measuring device that can detect (=project onto) an orthogonal basis of states, the probability of obtaining a certain ...
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How does technology rely on the probabilistic nature of quantum mechanics?

With respect to the dual slit experiment and the conclusion of probability waves, I was watching a documentary that said without "accepting chance" we couldn't have functioning technology in today's ...