What is Quantum mechanics: Definition and 995 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

    Other Senior Quantum Mechanics Research Project

    I am going to be doing a high school senior research project on how Quantum Physics will change the world in the future. Basically my current idea is to describe what quantum mechanics is, and then give examples that I explain and I state how they will change the world and the estimated time...
  2. L

    A States in usual QM/QFT and in the algebraic approach

    Studying QFT on curved spacetimes I've found the algebraic approach, based on ##\ast##-algebras. In that setting, a quantum system has one associated ##\ast##-algebra ##\mathscr{A}## generated by its observables. Here we have the algebraic states. These are defined as linear functionals...
  3. VIctor Medvil

    A SR/GRs Views on QM/QFT | Physics Forums

    This ties into this thread https://www.physicsforums.com/threads/i-want-to-know-the-exact-problems-of-merging-gr-and-qm.939509/ , I would like to know SR/GR's opinion of QM/QFT. I need both sides of the story.
  4. VIctor Medvil

    A I want to know the exact problems of Merging GR and QM

    This thread is I want a set of experts in the subject to show me the exact math of why Einstein's field Equations along with Special Relativity and Schrodinger's Equation along with deeper QM like QFT cannot be fused with GR. I want to see the exact anomalies in the equations myself from the...
  5. C

    I Question about inverse operators differential operators

    Hi all, so I'm not sure if what I'm asking is trivial or interesting, but is there any general or canonical way to interpret say, The follwing operator? (Specifically in the study of quantum mechanics): A = 1/(d/dx) (I do not mean d-1/dx-1, which is the antiderivative operator ) How would...
  6. J

    How to develop a method to reconstruct state in quantum mech

    Hi all, There is this question; Firstly, I am new to quantum mechanics and there are a lot of terms I am unfamiliar with. So there is this question that asks me to develop a method to reconstruct state and I have no clue how I should start with. Any help or steps to solve this type of...
  7. Curiose

    WaveGrid - Non-equilibrium Emergence Sandbox

    [Mentors' note: one short paragraph of speculation in violation of the Physics Forums rules has been removed from this post] Follow the link below to play with my experimental sandbox. The rest of this post includes some instructions for use and then observations and a little bit of theory...
  8. F

    Commutation Relation: Hi Parity Operator?

    hi, do the translation operator commute with parity operator?
  9. A. Neumaier

    I Classical chaos and quantum mechanics

    It is the resolution given by my thermal interpretation, and this resolution is valid (independent of the thermal interpretation) even without being accepted. Bell assumes that measurement outcomes follow strictly and with infinite precision Born's rule for a von Neumann measurement. But the...
  10. smodak

    Quantum Found a good set of lecture notes on Quantum Mechanics

    I am not sure whether this is posted before but it looks really good to me. http://www.tcm.phy.cam.ac.uk/~bds10/aqp.html
  11. ElanaC

    B Double slit experiment question

    Hi, I have two questions concerning the double slit experiment in the scenario where we fire one photon at a time and it interacts with itself to create an interference pattern over time: - Does the photon actually interact with itself or with the photons fired before/after it? - What happens...
  12. F

    I Is the Wavefunction Speed in Quantum Mechanics Wrong?

    This problem bothered me many years ago when I was taking a university course in quantum mechanics, but I assumed it was due to an error on my part which I, however, couldn’t locate, and I didn’t ask my course instructor about it. Recently, when researching a q.m. question on the Internet...
  13. PeterDonis

    Insights The Fundamental Difference in Interpretations of Quantum Mechanics - Comments

    Greg Bernhardt submitted a new PF Insights post The Fundamental Difference in Interpretations of Quantum Mechanics Continue reading the Original PF Insights Post.
  14. microsansfil

    I Principles of a Second Quantum Mechanics

    Hi all, Is there a critical analysis of this work ( https://arxiv.org/abs/1506.00431 ) that claims to develop a new representation of microstate and then using this representation as a reference-and-imbedding-structure, to develop a new foundations of an intelligible reconstruction of the...
  15. Pushoam

    Particle in a box quantum mechanics

    Homework Statement Homework EquationsThe Attempt at a Solution ## E \propto n^2 ## ## \frac { \Delta E} E = \frac { 2n +1} {n^2} ## In the limit of large quantum number, ## \frac { \Delta E} E = \frac { 2} {n} ##, option (a).
  16. Wrichik Basu

    Other Prerequisites for Internship in Quantum Mechanics

    I would be in college in 2019 (currently I'm in standard 11). I'm greatly interested in Quantum mechanics, QFT, QCD and Quantum Geometerodynamics. Of these, I want to do an internship on the first, because I don't think I'll be able to touch the others till the 2nd year in college. I'm living...
  17. Pushoam

    Force exerted by a particle in a box on the boundary

    Homework Statement Homework EquationsThe Attempt at a Solution The energy eigen - value of a particle in a box is given by ## E_n = \frac { n^2 h^2}{8mL^2} ## . Now, applying classical mechanics , ## \frac { p^2}{2m} = \frac { n^2 h^2}{8mL^2} ## . ## p \propto \frac { 1} L ## , So...
  18. B

    Contour integral and problem of Quantum mechanics (Griffiths)

    Homework Statement Homework Equations This is solution of Griffith problem 11.16 The Attempt at a Solution This is procedure to get a 1-D integral form of Schrodinger equation. I don't understand why that contour integral include only one pole for each contour?
  19. L

    Exploring the Intersection of Art and Physics: A Humanities Perspective

    Hi, I'm a new member. I joined this forum because I'm interested with astrophysics and cosmology. I'm actually in the field of the Humanities, currently taking up my Master's in Art History. I like physics because I think it is where art and science beautifully intersect. I started to see the...
  20. D

    Help Understanding the answer to a Quantum Mechanic problem

    Homework Statement The answer is as follows: [/B] However they said that time t=0 so I am confused how the exponent has a t in it surely it should be zero. Thanks
  21. 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...
  22. Gonv

    Probability of finding a particle in a region

    Homework Statement A particle is restrained to move in 1D between two rigid walls localized in ##x=0## and ##x=a##. For ##t=0##, it’s described by: $$\psi(x,0) = \left[\cos^{2}\left(\frac{\pi}{a}x\right)-\cos\left(\frac{\pi}{a}x\right)\right]\sin\left(\frac{\pi}{a}x\right)+B $$ , determine...
  23. S

    Forward light-cones and special relativity

    Homework Statement How can we tell that quantum effects do not propagate along forward light-cones that represent two separate events? How do light-cones demonstrate this notion of quantum effects? Homework EquationsThe Attempt at a Solution We don't know which events occur first given...
  24. C

    B Why doesn't this FTL communication scheme work?

    If Alice and Bob had a large number of particles entangled together (with state of either 0 or 1), could Alice send information by breaking the entanglement of particles with state of 1 (by flipping the state for example) so that Bob measures 50% of particles to be in the state opposite of 0...
  25. I

    I Meaning of Dirac Delta function in Quantum Mechanics

    If I have a general (not a plain wave) state $$|\psi\rangle$$, then in position space : $$\langle \psi|\psi\rangle = \int^{\infty}_{-\infty}\psi^*(x)\psi(x)dx$$ is the total probability (total absolute, assuming the wave function is normalized) So if the above is correct, does that mean...
  26. C

    A What are local and non-local operators in QM?

    In Hartree-Fock method, I saw the Fock operator has two integrals: Coulomb integral and exchange integral. One can define two operator. "The exchange operator is no local operator" why? Whats de diference: local and no local operator? And why do the operators have singularities? thanks
  27. smodak

    Quantum Found an interesting book on Quantum Mechanics

    and it is free (legal) Quantum Mechanics for Engineers by Dommelen
  28. Zafa Pi

    B Quantum Mechanics is not a theory?

    "... quantum mechanics isn’t a complete physical theory in its own right, but rather a framework for the construction of physical theories." I found this in Michael Nielsen's blog and elsewhere. I am perplexed. In what fundamental way does it differ from Newtonian Mechanics (Theory) in not...
  29. N

    "Protons+electrons" model vs "protons+neutrons" model

    Homework Statement Earlier in the book it was remarked that early in the history of nuclear physics the electrically neutral mass of nuclei now attributed to neutrons was considered to arise from neutral particles composed of combinations of protons and electrons (as opposed to neutrons in...
  30. A

    A Transformation of position operator under rotations

    In the momentum representation, the position operator acts on the wavefunction as 1) ##X_i = i\frac{\partial}{\partial p_i}## Now we want under rotations $U(R)$ the position operator to transform as ##U(R)^{-1}\mathbf{X}U(R) = R\mathbf{X}## How does one show that the position operator as...
  31. N

    Magnetic Moment and Spacing of Adjacent Magnetic Substates

    Homework Statement [/B] Consider the hydrogen atom in the 42F5/2 state. Take into account the effects of finestructure (spin-orbit coupling). (a) Write down the spectroscopic notation of the state that the 42F5/2 is degenerate with, in the absence of an external magnetic field. (b) Calculate...
  32. N

    Spectroscopic Notation Problem

    Question (a) Write down the quantum numbers for the states described in spectroscopic notation as 2S3/2, 3D2 and 5P3. (b) Determine if any of these states are impossible, and if so, explain why. (Please note that these could describe states with more than one electron.) My Attempt A) I came...
  33. A

    High Energy Recommended books in HEP, QFT, QM, GR

    Hi everyone! I'm trying to make a list of recommended books (introductory and advanced). So far, what I was able to search are the following: Particle Physics: - Griffiths: Introduction to Elementary Particles - Thomson: Modern Particle Physics - Nachtmann: Elementary Particle Physics -...
  34. N

    The Simulation Interpretation of Quantum Mechanics

    It seems like every argument in favor of the Simulation Hypothesis revolves around the strangeness of Quantum Mechanics. So can the Simulation Interpretation be just as valid of an interpretation as Copenhagen or Many Worlds? If not why not?
  35. M

    How Do You Calculate Eigenvalues for Combined Spins in Quantum Mechanics?

    Homework Statement Given 3 spins, #1 and #3 are spin-1/2 and #2 is spin-1. The particles have spin operators ## \vec{S}_i, i=1,2,3 ##. The particles are fixed in space. Let ## \vec{S} = \vec{S}_1 + \vec{S}_2 + \vec{S}_3 ## be the total spin operator for the particles. (ii) Find the eigenvalues...
  36. astrocytosis

    Eigenvalues and eigenvectors of a Hamiltonian

    Homework Statement The Hamiltonian of a certain two-level system is: $$\hat H = \epsilon (|1 \rangle \langle 1 | - |2 \rangle \langle 2 | + |1 \rangle \langle 2 | + |2 \rangle \langle 1 |)$$ Where ##|1 \rangle, |2 \rangle## is an orthonormal basis and ##\epsilon## is a number with units of...
  37. TheBigDig

    Expectation value of mean momentum from ground state energy

    1. The problem statement Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by H = \frac{p^2}{2m} + \frac{m \omega ^2 x^2}{2} Knowing that the ground state of the particle at a certain instant is described by the wave...
  38. A

    QM: Purity, two-outcome measurements

    Homework Statement Homework Equations in addition to those provided in the questions, I used the following: Tr(B) = sigma<x_j|B|x_j> purity = Tr(rho^2) The Attempt at a Solution [/B] I find calculating trace and purity very confusing. Am I on the right track with question 1? With...
  39. mr1batman

    How can i start in quantum physics and quantum mechanics?

    i want an article or video that i can start with at the journy of understanding the basics of quantum physics and quantum mechanics i don't want a book because in my country i would not find this types of books every where it's unique to find them thanks
  40. C

    I Probability vs radial density-confusion

    Hi everyone; A very stupid confusion here. When we want to talk about the most probable radius to find the electron in $1s$ orbital, why do we talk about the radial density and not the probability itself? For instance, the probability of finding the the electron at a radial distance $r$...
  41. N

    Solving for <p>, <x> and <x^2> using raising and lowering operators

    Homework Statement A) Show that <x>=<p>=0 hint: use orthogonality B) Use the raising and lowering operators to evaluate an expression for < x2 > Homework Equations Also A- and A+ will definitely come in handy The Attempt at a Solution I tried setting up the equations for <x> and <p> but I...
  42. N

    Virial Theorem and Simple Harmonic Oscillator

    Homework Statement Show that the virial theorem holds for all harmonic-oscillator states. The identity given in problem 5-10 is helpful. Homework Equations Identity given: ∫ξ2H2n(ξ)e-ξ2dξ = 2nn!(n+1/2)√pi P.S the ξ in the exponent should be raised to the 2nd power. So it should look like ξ2...
  43. N

    Lowering Operator Simple Harmonic Oscillator n=3

    Homework Statement Show that application of the lowering Operator A- to the n=3 harmonic oscillator wavefunction leads to the result predicted by Equation (5.6.22). Homework Equations Equation (5.6.22): A-Ψn = -iΨn-1√n The Attempt at a Solution I began by saying what the answer should end...
  44. N

    Rectangular Well Width and Next Higher Energy for Full Electron Transmission

    In an experiment involving electron scattering from a finite rectangular well of depth 4 eV, it is found that electrons of energy 5 eV are completely transmitted. What must be the width of the well? At what next higher energy can one expect to again observe T = 1? My Attempt: I used the...
  45. J

    A Do the equations of motion simply tell us which degrees of freedom apply?

    A massless spin 1 particle has 2 degrees of freedom. However, we usually describe it using four-vectors, which have four components. Hence, somehow we must get rid of the superfluous degrees of freedom. This job is done by the Maxwell equations. To quote from Gilmore's "Lie Groups, Physics, and...
  46. grandpa2390

    Determine state of particle: Quantum Mechanics (Phase)

    Homework Statement Homework EquationsThe Attempt at a Solution This is the Solution. I am having trouble understanding parts of it. The first part I don't get is why the e^i... goes with the -z. Did my professor just choose one at random, or is there a specific reason? The second part...
  47. grandpa2390

    Question about phase factor in Quantum Mechanics

    Homework Statement I am trying to understand a solution to a problem. I may not need to post the entire question, I just need to know if ##-i = e^{\frac{-i*pi}{2}}## Homework EquationsThe Attempt at a Solution the reason for this question is that one step of the problem has a quantity...
  48. S

    What are the latest developments in quantum mechanics?

    Hi fellow thinkers, my main area of interest is in QM. However I am always interested in new discoveries and experimental proofs of outstanding theories. Looking forward to joining the discussion with others who, like me, enjoy absorbing new information... S.P.W...
  49. K

    B How is Bohr's atom model convenient with quantum mechanics?

    Hi. From what I read, according to Quantum mechanics "even though it looks like objects are in definite places, when we get down to ridiculously tiny objects (like electrons) they seem to be not he in anyone place. And everything looks like a hazy clouds of probability."...
  50. Muthumanimaran

    Particle in one-dimensional harmonic oscillator

    Homework Statement This is a question asked in a entrance examination[/B] A charged particle is in the ground state of a one-dimensional harmonic oscillator potential, generated by electrical means. If the power is suddenly switched off, so that the potential disappears, then, according to...
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