# Quantum physics Definition and 145 Discussions

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
Classical physics, the description of physics that existed before the theory of relativity and quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, while quantum mechanics explains the aspects of nature at small (atomic and subatomic) scales, for which classical mechanics is insufficient. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).
Quantum mechanics arose gradually from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. These early attempts to understand microscopic phenomena, now known as the "old quantum theory", led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield.

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1. ### A Photon-Phonon Cavity Spectrum

I am considering the following Hamiltonian: $$H = -\Delta a^{\dagger}a + \omega_m b^{\dagger}b + g_0 * a^{\dagger}a (b + b^{\dagger})$$ which is the interaction picture optomechanical Hamiltonian for a cavity with movable end mirror. The mirror vibrations are quantized, leading to phonons that...
2. ### A Quantum weak measurement parameter estimation vs Classical Estimation

I am not an expert in quantum theory. I want to carry out some parameter estimation on a set of data I have. I have a model for the data with the parameter(s) of interest as variable(s). The data available is sporadic, meaning non-statistical or techniques involving no prior knowledge on the...
3. ### Quantum Need book recommendations for Quantum Chem/Nanomaterials

I am trying to learn about quantum chemistry for the purpose of understanding electronic structures of nanomaterials, or perhaps more generally some theoretical computational approaches to understanding interactions of nanomaterials/small molecules and high energy (keV to MeV) radiation. I'm...
4. ### Quantum Good resources for a beginner getting into Quantum Physics?

Summary:: I’m a beginner trying to get into Quantum Physics, and want some good resources (e.g. books) to get me started. Hi everyone! I’m a beginner trying to get into Quantum Physics, and want some good resources (e.g. books) to get me started. I have a very basic knowledge of physics (10th...
5. ### I How are good quantum numbers related to perturbation theory?

Hello folks, I am currently studying from Griffiths' Introduction to Quantum Mechanics and I've got a doubt about good quantum numbers that the text has been unable to solve. As I understand it, good quantum numbers are the eigenvalues of the eigenvectors of an operator O that remain...
6. ### Perturbation theory

Of course, this question consisted of two parts. In the first part, we needed to calculate the first-order correction. It was easy. In all the books on quantum mechanics I saw, only first-order examples have been solved. So I really do not know how to solve it. Please explain the solution method...
7. ### I Scientific realism and QM

I read in an article that "Quantum physics is a highly mathematical theory that describes the nature of reality at the atomic and subatomic level". I also read another article that says quantum physics does not tell anything about reality. Can you give me some context about it in a way that is...
8. ### I How is Coulomb's Law compatible with quantum physics?

In classical physics, we treat an electron as a point charge with a Coulomb potential ## V = \frac{q}{4\pi\epsilon_o r}##. However, in quantum mechanics, we treat it as an electron cloud. In this situation, how shall we describe the Coulomb potential? Shall we treat the electron as a charge...

10. ### I Functor between the category of Hilbert Space and the category of sets

I have a question that is related to categories and physics. I was reading this paper by John Baez in which he describes a TQFT as a functor from the category nCob (n-dimensional cobordisms) to Vector spaces. https://arxiv.org/pdf/quant-ph/0404040.pdf. At the beginning of the paper @john baez...
11. ### I Is there any physical significance to Wave Amplitude?

I am studying Quantum physics and I'm having some problems to understand what is the Wave Amplitude since I can't find a physical significance to it. Does anyone ever heard something that come close to a physical significance?
12. ### A Interface between Biological Physics and Quantum Physics

Are there areas of studies which could be characterized as an interface of biological physics and quantum physics? Does such an interface even exist?
13. ### I Complex Conjugate of Wave Function

I've been studying quantum mechanics this semester in school and have ran into an issue I can't find an answer for. I understand why we take the complex conjugate of the wave function, such as when calculating expectation values. I'm a little confused though as to why we take the complex...
14. ### I What'wrong in this argument? (Atom/Photon interferometry)

First, we can think a MZ interferometer as a combination of two beamspliter and a phase shifter(from MIT course "Atomic and Optical Physics II", the paper is "Quantum-mechanical noise in an interferometer"), which evolution matrix is B = {{1,-i},{-i,1}},B dagger and P ={{1,0},{{0,exp{i\phi}}}...
15. ### What's the Real Meaning of Quantum Mechanics? - with Jim Baggott

Jim explores what are the most popular interpretations of quantum mechanics and how we might need to be a little more specific when we talk about ‘reality’. Excellent layman's explanation of the Bell Inequality experiments.
16. ### Help with this quantum circuit textbook problem about controlled gates

Summary:: My skills are very very basic and i'm more a networking major but i had to take a quantum mechanics class, i have trouble with this xcercise from textbook quantum mechanics a general introduction [Mentor Note -- Thread moved from the Technical forums so no Homework Template is shown]...
17. ### Finite quantum well, multiple choice question

Homework Statement:: Consider an electron trapped in a one-dimensional finite well of width L. What is the minimum possible kinetic energy of the electron? A) 0 B) Between 0 and h^2/8mL^2 C) ≈h^2/8mL^2, but it is not possible to find the exact value because of the uncertainty principle D)...
18. ### Studying Self-studying plan for modern science

Hey guys, I want to build a strong and straight plan for my next years of studying and once finish I am able to do something on my own and come up with crazy ideas and actually test them, build some awesome algorithms, all that cool stuff, but I'm kinda stumble so it would be nice if someone...
19. ### A Simultanious eigenstate of Hubbard Hamiltonian and Spin operator in tw

Please see this page and give me an advice. https://physics.stackexchange.com/questions/499269/simultanious-eigenstate-of-hubbard-hamiltonian-and-spin-operator-in-two-site-mod Known fact 1. If two operators ##A## and ##B## commute, ##[A,B]=0##, they have simultaneous eigenstates. That means...
20. ### Shelf in a box, treating the shelf as a weak perturbation

In this problem I am supposed to treat the shelf as a weak perturbation. However it doesn't give us what the perturbed state H' is. At the step V(x) = Vo, but that is all that is given and isn't needed to determine H'. This isn't in a weak magnetic field so I wouldn't you use H'=qEx and then...
21. ### Constant of proportionality in probability of superposition of states

Using the fact that Pa ∝ |α|^2 and Pb ∝ |β|^2, we get: Pa = k|α|^2 and Pb = k|β|^2 Since the probability of measuring the two states must add up to 1, we have Pa + Pb = 1 => k = 1/(|α|^2 + |β|^2). Substituting this in Pa and Pb, we get: Pa = |α|^2/(|α|^2 + |β|^2) and Pb = |β|^2/(|α|^2 + |β|^2)...
22. ### I Relation between the momentum operator and the Hamiltonian gradient operator

Is there a relationship between the momentum operator matrix elements and the following: <φ|dH/dkx|ψ> where kx is the Bloch wave number such that if I have the latter calculated for the x direction as a matrix, I can get the momentum operator matrix elements from it?
23. ### How to find von-Klitzing constant based on graph?

Hi all, Given that the question: From what i know , im not sure how this equation can help me estimate the von-klitzing constant? Or is there another way? Thanks!
24. ### A LS vs jj couplings and their selection rules

Two questions, where the 1st is related to previous discussion regarding thes couplings: The selection rules for LS coupling is quite clear - it's based on calculating the compatible electric dipole matrix element. However, in the case of jj coupling we end up with different selection rules...
25. ### I Confusion on binding energy and ionization energy.

1) I know that the binding energy is the energy that holds a nucleus together ( which equals to the mass defect E = mc2 ). But what does it mean when we are talking about binding energy of an electron ( eg. binding energy = -Z2R/n2 ? ). Some website saying that " binding energy = - ionization...
26. ### I David Deutsch (1985) attempt to solve the incoherence problem

Can anyone elaborate on Deutsch's attempt to solve the incoherence problem? He postulates a continuously infinite set of universes, together with a preferred measure on that set. And so when a measurement occurs, the proportion of universes in the original branch that end up on a given branch...
27. ### Insights A Classical View of the Qubit - Comments

Greg Bernhardt submitted a new blog post A Classical View of the Qubit Continue reading the Original Blog Post.
28. ### B Quantum entanglement phenomenon

Hi there, Question from a biologist with very poor background in physics, but willing to understand quantum physics. I think quantum entanglement shocks everyone, even if it has been proven right. I would love to know if there is any hypothesis or crazy theory out there to explain why or how...
29. ### Against "interpretation" - Comments

Greg Bernhardt submitted a new blog post Against "interpretation" Continue reading the Original Blog Post.
30. ### I Van der Waals force in quantum physics

According to QFT, are there hydrogen bonds or Van der Waals force? Or this an outdated concept of classical physics?
31. ### Insights The Quantum Mystery of Wigner's Friend - Comments

Greg Bernhardt submitted a new blog post Wigner's Friend Continue reading the Original Blog Post.
32. ### A Quantization of the electric field inside a box

Hello all, The second quantization of a general electromagnetic field assumes the energy density integration to be performed inside a box in 3D space. Someone mentioned to me recently that the physical significance of the actual volume used is that it should be chosen based on the detector used...
33. ### Insights The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations - Comments

Greg Bernhardt submitted a new blog post The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations Continue reading the Original Blog Post.
34. ### I Causality and quantum physics

Let me present what I think is the understanding of a particular situation in quantum mechanics, and ask people to tell me whether I am right or wrong. To say that everything happens randomly in QM would be misleading at best. We get at least statistical prediction. But discussions such as the...
35. ### Expectation value <p> of the ground state of hydrogen

Homework Statement How should I calculate the expectation value of momentum of an electron in the ground state in hydrogen atom. Homework Equations The Attempt at a Solution I am trying to apply the p operator i.e. ##-ihd/dx## over ##\psi##. and integrating it from 0 to infinity. The answer I...
36. ### I Dressed electrons are not defined as point masses...

In @A. Neumaier 's excellent Physics FAQ, he notes under "Are electrons pointlike/structureless?" that "Physical, measurable particles are not points but have extension. By definition, an electron without extension would be described exactly by the 1-particle Dirac equation, which has a...
37. ### Finding state vectors for pure states!

Homework Statement Is the following matrix a state operator ? and if it is a state operator is it a pure state ? and if it is so then find the state vectors for the pure state. If you dont see image here is the matrix which is 2X2 in matlab code: [9/25 12/25; 12/25 16/25] Homework...

41. ### Harmonic Oscillator violating Heisenberg's Uncertainity

Homework Statement Does the n = 2 state of a quantum harmonic oscillator violate the Heisenberg Uncertainty Principle? Homework Equations $$\sigma_x\sigma_p = \frac{\hbar}{2}$$ The Attempt at a Solution [/B] I worked out the solution for the second state of the harmonic oscillator...
42. ### I Can something be caused and be ontologically random?

Or does ontological probability exist? I was reading an article that came up in my google searches ( https://breakingthefreewillillusion.com/ontic-probability-doesnt-exist/ ) ignore the free will philosophy stuff. But the author makes the claim that ontological probability simply does not...
43. ### I Einstein-Bohr "photon box" debate and general relativity

I see this has been already discussed but the old threads are closed. EPR before EPR: a 1930 Einstein-Bohr thought experiment revisited "In this example, Einstein presents a paradox in QM suggesting that QM is inconsistent, while Bohr attempts to save consistency of QM by combining QM with the...
44. ### Insights Interview with Astrophysicist: Adam Becker - Comments

Greg Bernhardt submitted a new PF Insights post Interview with Astrophysicist: Adam Becker Continue reading the Original PF Insights Post.
45. ### Reason for the speed of light

Is it possible that the speed of light exists because we cannot move faster than our particles? I.e. the speed of electrons that create the electromagnetic force that hold matter together.
46. ### B Explanation of Quantum Entanglement Please

Hello, I am 12 years old in 6th grade and love physics and Quantum Physics, I would love an explanation of Quantum Physics and Topological Quantum Matter.
47. ### I Particles as matter waves

Hi at all, i've the following question: How the fondamental particles (electrons, protons) are seen as matter waves, what shape and size should be these waves? They are wave-packets?
48. ### A Wavelength of the pilot wave

Hi, I am new to the Pilot Wave theory. In my understanding this theory gives a hope for reconstruction of the realism. But I have several maybe naif questions. What is the wavelength of the pilot wave? Is it the same as deBroglie wavelength formula? Very often people use the walking droplets...
49. ### A Why do space translations satisfy the Wigner's Theorem?

Some books argue that typical coordinate transformations such as space translations and rotations are represented in quantum mechanics by unitary operators because the Wigner's theorem. However I do not find any clear proof of this. For instance, suppose 1D for the sake of simplicity, by...
50. A

### B Planck-Einstein relation and the Photoelectric Effect

Hi everyone, I just have some confusion regarding Planck's and Einstein's equation. The following is an explanation of the photoelectric effect using Einsteins theory: Light is composed of photons. Each photon has energy hf and mass hf/c^2. When ultraviolet photons are brought to rest by zinc...