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21
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7answers
2k views

Why is the application of probability in QM fundamentally different from application of probability in other areas?

Why is application of probability in QM fundamentally different than application of probability in other areas? Quantum mechanics applies probability according to the same probability theory that ...
8
votes
4answers
3k views

Infinite universe - Jumping to pointless conclusions

I watched an episode of thee BBC Horizon series titled 'To infinity and beyond'. In this program a number of respected physicists and mathematicians were talking about the nature of infinity and an ...
5
votes
3answers
382 views

Probability and probability amplitude

The equation: $$P = |A|^2$$ appears in many books and lectures, where $P$ is a "probability" and $A$ is an "amplitude" or "probability amplitude". What led physicists to believe that the square of ...
8
votes
5answers
705 views

Born rule and unitary evolution

Is the Born rule a fundamental postulate of quantum mechanics, or can it be inferred from unitary evolution?
7
votes
3answers
833 views

Born's Rule, What is the Reason?

As far as I've read online, there isn't a good explanation for the Born Rule. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives ...
6
votes
6answers
5k views

Probability amplitude in Layman's Terms

I am basically a Computer Programmer, but Physics has always fascinated and often baffled me. I have tried to understand probability density in Quantum Mechanics for many many years. What I ...
5
votes
4answers
603 views

What is the difference between + and - signs in superpositions of quantum states?

What is the difference between states $$ \frac1{\sqrt{2}} |11\rangle+\frac1{\sqrt{2}} |00\rangle $$ and $$ \frac1{\sqrt{2}} |11\rangle- \frac1{\sqrt{2}} |00\rangle~? $$ They will all eventually ...
5
votes
5answers
7k views

Would one actually find their doppleganger in a “Googolplex Universe”?

Related: Infinite universe - Jumping to pointless conclusions I've recently become a fan of Numberphile, and today I happened to watch their video regarding Googol and Googolplex. In the video, ...
4
votes
3answers
329 views

Are negativity of the Wigner function and quantum behaviour equivalent?

I've read the following question: Negative probabilities in quantum physics and I'm not sure I understand all the details about my actual question. I think mine is more direct. It is known that the ...
3
votes
3answers
554 views

Wavefunction, probability and impossible events

A friend of mine asked me a question, which I considered trivial at first, but after a while gave rise to some doubts. For instance, we have a potential well in 1 dimension defined by $$ V(x)= ...
3
votes
2answers
571 views

an example of a quantum system for which wigner function transitions to negative values

I want to check my understanding of the Wigner transform and try to understand why and how exactly the probabilistic interpretation drops down as the function goes to zero and then to negative values ...
7
votes
3answers
1k views

Relation between unitarity and conservation of probability

In a seminar, I heard that the unitary aspect of representations was important physically, because in quantum mechanics unitarity is closely tied to the conservation of probability. Could someone ...
5
votes
3answers
265 views

Why, in spin sums, we sum over final spin states and average over initial states?

I am reading Halzen's book about quarks and leptons and on page 120 he talks about spin sums. He says that in order to calculate the amplitude between unpolarized states we have to sum over FINAL ...
3
votes
2answers
253 views

Are probability-preserving variations of QT with respect to the Born rule mathematically possible?

Is it possible to create (m)any theoretically workable framework(s) - that do(es) produce probabilities - by taking QM and replacing the Born(-like) rule(s) with something that is not equivalent to it ...
3
votes
1answer
611 views

Transmission and reflection

What is the transmission amplitude of a wavefunction $\phi(x)=e^{ikx}(\tanh x -ik)$? I would have thought that it is $\tanh x -ik$ since this is the factor associated with the forward travelling ...
0
votes
2answers
60 views

Probability from classical physics compared with quantum mechanics [closed]

$|\psi\rangle$=$\frac{1}{\sqrt5}|\uparrow_z\rangle+\frac{2}{\sqrt5}|\downarrow_z\rangle$ a)What is the probability of obtaining $+\frac{\hbar}{2}$ for $S_x$? b)If after obtaining ...
9
votes
2answers
557 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 ...
8
votes
3answers
953 views

Determinism, classical probabilities, and/or quantum mechanics?

[I]f you want a universe with certain very generic properties, you seem forced to one of three choices: (1) determinism, (2) classical probabilities, or (3) quantum mechanics. [My emphasis.] ...
8
votes
1answer
433 views

How to determine the probabilities for a cuboid die?

Imagine we take a cuboid with sides $a, b$ and $c$ and throw it like a usual die. Is there a way to determine the probabilities of the different outcomes $P_{ab}, P_{bc}$ and $P_{ac}$? With $ab$, ...
7
votes
2answers
1k views

Particle in a 1-D box and the correspondence principle

Consider the particle in a 1-d box, we know very well the solutions of it. I'd like to see how the correspondence principle will work out in this case, if we consider position probability density ...
6
votes
3answers
479 views

Could quantum mechanics work without the Born rule?

Slightly inspired by this question about the historical origins of the Born rule, I wondered whether quantum mechanics could still work without the Born rule. I realize it's one of the most ...
3
votes
0answers
169 views

Moments of a Distribution via Laplace Transforms and Wick Rotations [closed]

On a mathematical level, the statistical mechanical partition function is just a Laplace transform of the microcanonical probability distribution, i.e. it's moment generating function. Understanding ...
0
votes
5answers
306 views

Why do we need a wave function?

Assuming our only aim is to solve double slit experiment (or other problems that can be mapped into that). Knowing that electron does some strange thing not expected of a particle, we need a function ...
7
votes
2answers
319 views

Interpretation: probability form probability amplitude (free particle)

If you compute the probability amplitude of a free 1D non-relativistic particle with mass $m$, located at position $x_0$ at time $t_0$, for beeing detected at some other point $x_N$ at time $t_N$ you ...
2
votes
3answers
215 views

Probability distribution in phase space and Liouville's theorem?

We can define a probability distribution over phase space (say 1D) $\rho(x,p)$ such that, for example, $$\langle x\rangle = \int x \rho(x,p) dxdp$$ etc. It can be shown here that such a distribution ...
2
votes
3answers
275 views

How to show that probability and statistics are very important in Quantum Mechanics?

I'm doing a research for my stats class in high school and I chose quantum mechanics as my subject. I narrowed down to electron localization in an atom and radial probability distribution. However, I ...
1
vote
1answer
682 views

Probability, quantum physics, and why (can't it/does it) apply to macroscale events?

Quantum physics dictates that there are probabilities that determine the outcome of an event, ie: the probability of a quark passing through a wall is X, due to the size of the quark in comparison to ...
11
votes
1answer
533 views

The measure problem in the anthropic principle

The anthropic principle is based upon Bayesian reasoning applied to the ensemble of universes, or parts thereof, conditioned upon the existence of conscious observers. That still leaves us with the ...
9
votes
3answers
1k views

What is the relationship between Maxwell–Boltzmann statistics and the grand canonical ensemble?

In the grand canonical ensemble one derives the expectation value $\langle \hat n_r\rangle^{\pm}$ for fermions and bosons of sort $r$: $$ \langle \hat n_r\rangle^{\pm} \ \propto \ ...
5
votes
3answers
291 views

Physical intuition for independence of components of velocity in derivation of Maxwell–Boltzmann distribution

Maxwell derived the shape of the probability distribution of velocity of gas particles by starting with just two assumptions. These are: The probability distribution is rotation invariant. The ...
3
votes
2answers
2k views

How do I figure out the probability of finding a particle between two barriers?

Given a delta function $\alpha\delta(x+a)$ and an infinite energy potential barrier at $[0,\infty)$, calculate the scattered state, calculate the probability of reflection as a function of ...
2
votes
0answers
299 views

Probability and probability amplitude [duplicate]

What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
2
votes
1answer
183 views

Can someone explain probability flux in the tunneling boundary condition of Vilenkin?

This is what's leading to the notion of a quantum universe tunneling from nothing into existence, right? The idea is that probability flux flows out of superspace (configuration space) at ...
1
vote
3answers
184 views

Intuition/derivation behind the probability current definition

The definition is: $${\bf{j}} = \frac{\hbar}{2mi} (\psi^* \nabla \psi - \psi \nabla \psi^*)$$ However: Where ever I have looked, the above "pops out of nowhere". I was wondering how can I obtain ...
1
vote
1answer
163 views

Expectation values in QFT?

What is the meaning of different expectation values in QFT? For instance: $$\langle 0|{\cal O}(0)|q,s\rangle$$ or $$\langle 0|{\cal O}(0)|0\rangle$$ with ${\cal O}$ being some operator and ...
1
vote
0answers
77 views

Equivalence of simple formulations of qubit entanglement

I'm reading some very elementary treatments of quantum computation and am unsure about the correspondence among "definitions" of qubit entanglement. One definition states that (1) the bits of a ...
6
votes
2answers
308 views

Mathematical probabilistic interepretation of probability amplitude

As a warning, I come from an "applied math" background with next to no knowledge of physics. That said, here's my question: I'm looking at the possibility of using probability amplitude functions to ...
5
votes
2answers
544 views

Is it really impossible to calculate in advance the result of throwing dice?

Is it really impossible to calculate in advance the result of throwing dice? After all, the physics of dice throwing is in the world of classical mechanics, rather than quantum mechanics.
4
votes
1answer
248 views

Young's double slit

Am I right to think the (general) probability distribution of photon in a double slit experiment at the screen has the form $|\psi|^2 = c e^{\alpha x^2}\cos^2(\beta x)$? (Due to the superposition of ...
4
votes
1answer
185 views

Products of Gaussian stochastic process variables

In the classic experimental physics text "Statistical Theory of Signal Detection" by Carl. W. Helstrom, Chapter II, section 4 concerns Gaussian Stochastic Processes. Such a process is observed at ...
3
votes
1answer
62 views

Probability of photon emission

If a photon of a given wavelength is absorbed by an electron (for simplicity, let's assume the electron has only one excited state), does the probability that the electron jumps to its excited state ...
3
votes
2answers
118 views

How to calculate the tree-level probability amplitude for the electron-positron to muon-antimuon process?

Consider the following process: $e^+ + e^- \rightarrow \mu^+ + \mu^-$. I'm trying to calculate the probability amplitude of such a process in leading order. In leading order the amplitude is given ...
3
votes
2answers
164 views

Free-particle solution to Schrödinger Equation

The free particle solution in stationary state (with definite energy) to the Schrödinger equation is $$\psi(x,t) =Ae^{i(kx-\omega t)} + Be^{-i(kx+\omega t)}$$ Since the energy is definite, and ...
2
votes
1answer
730 views

Probability of finding n particles in a volume v

I'm trying to calculate the probability of finding $n$ particles in a certain volume $v$ in a system with a total of $N$ particles and total volume of $V$. My problem is that I've tried two approaches ...
2
votes
1answer
135 views

Basic question about probability and measurements

Say I have a Galton box, i.e. a ball dropping on a row of solid bodies. Now I want to calculate the probability distribution of the movement of the ball based on the properties of the body (case A). ...
2
votes
1answer
2k views

Probability current

Conservation of probability: Suppose a wavefunction has ${\partial \mathbb P \over \partial t} = -t f(x,t)$ and ${\partial j \over \partial x} = i f(x,t)$. How does it follow that ${\partial \mathbb P ...
0
votes
1answer
75 views

Why are transition amplitudes more fundamental than probabilities in quantum mechanics? [duplicate]

I am reading Quantum Theory: Concepts and Methods by Asher Peres. Terminology used in the book: $P_{\mu m}$ are "transition probabilities". They are the squares of "transition amplitudes". That is, ...
0
votes
1answer
56 views

How was phase randomly changing in CHSH test (M. A. Rowe and others)?

Measuring phase of photon should always be random while checking CHSH inequality, but i can't explain this: http://qudev.ethz.ch/content/courses/QSIT08/pdfs/Rowe01.pdf (the most clear experiment i ...
0
votes
2answers
57 views

Calculating the Probability Current of a Travelling Wave

Calculate the probability current density vector $\vec{j}$ for the wave function : $$\psi = Ae^{-i(wt-kx)}.$$ From my very poor and beginner's understanding of probability density current it is : ...
0
votes
1answer
805 views

Plotting Hydrogen's $2P_{x,y,z}$ Probability Densities in MATLAB [closed]

I have spent an unreasonable amount of time trying to plot $F(r,\theta,\phi)$ plane slices in MATLAB. I want to look at $x-y,y-z,x-z$ planes. Here's the function, specifically: ...