# Tagged Questions

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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### Probability density of a trig function [on hold]

I have a problem: I'm given that the needle on a speedometer is broken, free to move, and equally likely to be found at any point between $0 < \theta < \pi$ So, obviously the probability ...
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### Why must the separation constant be real in a time dependent wave function?

I'm not sure if I'm asking this right. I'm reading ''Introduction to Quantum Mechanics'' by Griffiths and in the chapter 2 exercises he asks to prove that the separation constant, $E$, must be real. ...
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### Can we predict throwing a dice?

What happens if we throw a dice from same position, with same force, by creating a vacuum environment on earth? Will it be predictable now i.e. will the dice have same results all the time? If answer ...
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### Why Does the Dirac delta Function Fix the Normalization of the Basis Vectors in Infinite Dimensions? [duplicate]

On page 60 of Shankar's intro to QM at the very bottom he says that the Dirac delta function fixes the normalization of the basis vectors with an infinite amount of dimensions. I don't understand why ...
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### Finance-Physics Rosetta Stone [on hold]

Does there exist, or can anyone provide, a translation between the language of financial maths and physics (specifically option pricing vs. diffusion)? I'm interested in Ito diffusion but a lot of ...
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### ploting probability distribution of energy in Canonical ansambel [closed]

To reproducing fig3.3 statistical mechanics pathria, probability density function of energy: $$p(E)\quad \alpha \quad e^{-\beta E} g(E) = e^{-\beta (U-TS)}~ exp{(-\frac{(E-U)^2}{2KT^2C_V})}$$ . I ...
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### 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 ...
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### Diffusion Equation for Particle Hopping with drift

First of all, I haven't studied partial differential equations yet, hence this question might sound silly. I am doing a simulation for particle hopping on a lattice with python. I was said that in ...
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The density matrix of the system is given by: $$[\rho_{S}(t)]_{mn} = [\rho_{S}(0)]_{mn} e^{-i\omega_{0}(m - n)t} e^{-i \delta(t)(m^2 - n^2) - \gamma(t)(m - n)^2}, ... 7answers 1k views ### Why is a Hermitian operator a “quantum random variable”? To me, as a stupid mathematician, a random variable is a measurable function from some probability space (\Omega, \sigma, \mu) to (\Bbb{R}, B(\Bbb{R})). This makes sense. You have outcomes, events,... 3answers 1k views ### Feynman random walk In Richard Feynman's lectures on physics, chapter six, part 3, he explains something called the random walk, in which, in a succession of trials, a system moves forward one step or backward by one ... 1answer 134 views ### Is it possible to build a logical theory in QM based on quantum logic? [closed] Quantum Probabilities as Bayesian Probability, Quantum probabilities as degrees of belief Above are two articles about quantum Bayesianism. I don't know why quantum Bayesianism use some results from ... 1answer 204 views ### Probability and double slit if a beam of identical particles at random distances from each other (or exactly 1/2 lambda between each other) travelling with the same v towards a double sllit do not interfere with each others wave ... 0answers 15 views ### talking of probability(of a random variable distribution) at a point [migrated] "Suppose a species of bacteria typically lives 4 to 6 hours. What is the probability that a bacterium lives exactly 5 hours? The answer is actually 0%. A lot of bacteria live forapproximately 5 hours, ... 1answer 112 views ### Has Jaynes' argument for quantum mechanics as a possible theory of inference been debunked? To my understanding, there is currently no scientific consensus on which interpretation of quantum physics is the correct one, if any. The most famous one, perhaps for historical reasons, is the ... 1answer 24 views ### Why is collision of electrons different from alpha particles in terms of probability amplitude? In The Feynman lectures on physics volume 3, chapter 3, page 3-11, there is the following paragraph: An even more perplexing thing happens when we do the same kind of experiment by scattering ... 3answers 450 views ### Normalization of wave function meaning…? I just have one question. I'm doing a problem where I'm told to normalize a wave function, which is split up into two regions, namely where r \leq r_0 and r > r_0. My question is, why am I ... 8answers 3k views ### Why is the application of probability in QM fundamentally different from application of probability in other areas? Why is the application of probability in quantum mechanics (QM) fundamentally different from its application in other areas? QM applies probability according to the same probability axioms as in other ... 2answers 135 views ### What does the continuity equation for probability in quantum mechanics mean? In quantum mechanics, the continuity equation -{d\rho}/{dt}=\nabla\cdot{J} holds for a probability density \rho and probability current J. But what does it mean, from a physical point of view? ... 2answers 39 views ### Fermi-Dirac distribution - holes and electrons The density of probability of an energy state E being occupied by an electron is$$f(E,T)=\frac{1}{1+e^{\frac{E-E_F}{kT}}}$$and the density of probability of an energy state being occupied by a ... 0answers 1k views ### tritium beta decay - probability of being in 1s state Hydrogen-like wavefunctions have the form:$$R_{10} = \left(\frac{Z}{a_0}\right)^{\frac{3}{2}} 2\space e^{-\frac{Zr}{a_0}}Y_{00} = \frac{1}{\sqrt {4\pi}} $$where a_0 = \frac{4\pi \epsilon_0 \... 0answers 37 views ### Probability of measuring a pure qubit state after some unitary rotation [closed] Suppose I have the prepared state$$|+\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}}$$and the unitary Z_{\pi/2} which rotates a state in the Bloch sphere by +\pi/2 about the z-axis. As I ... 0answers 35 views ### probability of striking the circular ring by gas molecules In kinetic theory we use probabilistic case to derive pressure, no. Of molecules having speed c to c+dc or in such cases.and to derive such equations we introduce a term called "SOLID ANGLE" I come ... 1answer 44 views ### probability of finding the system in the ground state [closed] \renewcommand{\ket}[1]{\left \lvert #1 \right \rangle} Assume that a quantum mechanical system is described by two orthonormal states \ket{+} and \ket{-}, defined by the property of being ... 4answers 2k views ### What is a wave function in simple language? In my textbook it is given that 'The wave function describes the position and state of the electron and its square gives the probability density of electrons.' Can someone give me a very ... 0answers 60 views ### Measurement of L_z in a state which includes spin I'm working through a problem on finding probabilities for measurements performed for quantities associated with one electron in three dimensions with spin. In that case we know that the state space ... 2answers 53 views ### What makes the probability distribution of a wavefunction in QM intrinsic? [closed] I know that the usual interpretation of the wavefunction in QM is that it´s associated with a probability distribution of measurable quantities. Not a deterministic probability (like the probabilities ... 1answer 51 views ### Multiplication of associated probabilities If a state \psi  is in the  S_{z}  basis represented by \mid\psi\rangle = c_{+}\mid z\rangle + c_{-} \mid -z\rangle Does the associated probabilities change when I multiply  \psi  by  e^{i\... 0answers 70 views ### Time Scales Of Processes In Molecular Dynamics Suppose I run a molecular dynamics simulation of a fluid sandwiched between solid walls which are periodic in the lateral directions and finite in the direction of the fluid film thickness. Now, I ... 1answer 33 views ### Why is the standard deviation the error on the singular measurement? I'm a beginner with the study in data analysis in Physics. I'm trying to understand the meaning, in the field of experimental Physics, of the standard deviation \sigma of a series of data. There ... 1answer 17 views ### Mach-Zehnder probabilities Where can I find the computations of probabilities for Mach-Zehnder experiments, say at the undergraduate level? For example I'm thinking of the type of experiments described at the beginning of David ... 0answers 19 views ### Derivation of generation of time between two subsequent particle enters into computational domain I have problem with understanding derivation of one equation in following problem. You have 1D computational domain (it is not 1D but because it is symmetrical and we are watching only radial ... 6answers 1k views ### Why was quantum mechanics regarded as a non-deterministic theory? It seems to be a wide impression that quantum mechanics is not deterministic, e.g. the world is quantum-mechanical and not deterministic. I have a basic question about quantum mechanics itself. A ... 0answers 72 views ### What's the probability distribution of a deterministic signal or how to marginalize dynamical systems? In many signal processing calculations, the (prior) probability distribution of the theoretical signal (not the signal + noise) is required. In random signal theory, this distribution is typically a ... 0answers 63 views ### How did Max Born come up with his rule? [duplicate] In his rule, he stated that the probability is norm-squared of wave function, |\psi|^2. And as far as I knew, no one else at that time had "right" interpretation of the wave function. Even ... 0answers 31 views ### Is there a Bayesian theory of deterministic signal? Prequel and motivation for my previous question This is a prequel to my question: What's the probability distribution of a deterministic signal or how to marginalize a dynamical system? Clearly my question looks at the same time fairly ... 1answer 41 views ### Conservation of energy and realm of possibility The law of conservation of energy states that energy cannot be created or destroyed. Based on this principle, you can safely conclude that any effect resulting from a cause must somehow keep all ... 1answer 23 views ### Relation between probability density and transmission probability of a wavefunction? Problems I did on current densities in elementary quantum mecanics course gives the answer contains transmission coeffecients, I am wondering is there any relation among them. 2answers 78 views ### If I repeated a quantum measurement, would it be the same? [closed] I was thinking about the probabilistic nature of quantum mechanics and that if I measured the position of an electron twice in succession, the outcomes would depend on a probability. However, what if ... 2answers 118 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 ... 0answers 40 views ### Relevance of pure mathematics vs statistics to physics [closed] For someone currently studying physics, with an interest in experimental physics, would pure mathematics or statistics be more relevant? 1answer 46 views ### Multiple measurements and the any worlds interpretation My question has some similarities to but also differs significantly from this question which was described in many of its answers as not being a quantum mechanical measurement and was I think, ... 0answers 27 views ### How can absorbtion of a photon in an atom take place? [duplicate] I will come back to a question posed here and the comment given by John Rennie: If the photon energy doesn't match an allowed transition energy it won't be absorbed and won't excite any transition. ... 0answers 14 views ### Counting the accesible microestates compatible with the macrostate conditions Let be a system consisting of N magnetic dipoles with magnetic dipole \vec{\mu} in a magnetic field \vec{B}. I want to count the micro states accessible to the macro estate defined by E=-\mu B ... 0answers 20 views ### Does it make sense to add overlapping probabilities > 1? I read about a variation of Bell's inequality, expressed as$$P_\text{same}(A, B) + P_\text{same}(A, C) + P_\text{same}(B, C) ≥ 1$$It is later shown that the inequality is violated using QM. ... 1answer 53 views ### Why does this formula for the partition function not include the multiplicity? I am having problems understanding the formulas used for describing the partition functions and the probability distributions for canonical ensembles. In the first case I have two formulas for the ... 1answer 47 views ### How to calculate probability of complex wave functions? [closed] An election has an equation as such:$$Ψ(x) = e^{iαx^2}.$$How am I supposed to find the probability of finding the electron over a certain range? Is Fourier Transform involved in this? 2answers 48 views ### Quantum Mechanics: Can the probability of finding a particle in the whole space be smaller or higher at certain times? In the book Introduction to Quantum Mechanics (by David Griffith) there is an Example 2.1: Suppose a particle starts out in a linear combination of just two stationary states:$$\Psi(x,0)~=~c_1\...
Consider a real scalar quantum field $\varphi (x)$, interacting with a classical real scalar field $J(x)$ : $$\mathcal{L} = \frac{1}{2}(\partial \varphi)^2 - \frac{m^2}{2} \varphi^2 + \varphi J$$ ...