Quantum mechanics Definition and 994 Threads

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. P

    Normalization of the Angular Momentum Ladder Operator

    Homework Statement Obtain the matrix representation of the ladder operators ##J_{\pm}##. Homework Equations Remark that ##J_{\pm} | jm \rangle = N_{\pm}| jm \pm 1 \rangle## The Attempt at a Solution [/B] The textbook states ##|N_{\pm}|^2=\langle jm | J_{\pm}^\dagger J_{\pm} | jm \rangle##...
  2. TheSodesa

    A gyromagentic ratio for a cylinder

    Homework Statement In classical physics, a system's magnetic moment can be written like so: \mu = g\frac{Q}{2M}L, where ##Q## is the total charge, ##M## is the total mass of the system and ##L## the angular momentum. a) Show, that for a cylinder (##I = \frac{1}{2}MR^2##) spinning around its...
  3. Eureka99

    Where to Find the Best Quantum Mechanics Resources?

    Hi everyone, I wanted to know if any of you knows very good sources for quantum mechanics and spectroscopy fundamentals, like greats books, youtube videos (lectures), or any other option. I' m studying spectroscopy at the moment, and last year I've done the Physical Chemistry II course ( quantum...
  4. C

    Measurement standard for joules = Momentum in kilograms

    Basically, I found the energy of a photon using its frequency ((6.8*10^15) and E=(3.6496394*10^-16)) and so I then used "p=E/c" to find the momentum and got 1.2173887*10^-24 however I don't know the measurement of the momentum. Is there a better equation to use to find momentum, and what would...
  5. S

    A Adiabatic process - quantum mechanics and thermodynamics

    A diabatic process is defined as follows: Rapidly changing conditions prevent the system from adapting its configuration during the process, hence the spatial probability density remains unchanged. Typically there is no eigenstate of the final Hamiltonian with the same functional form as the...
  6. Avimanyu Ray

    Quantum Starting books for Quantum Mechanics

    Hello I'm an undergrad. Can anyone suggest me books, articles, lectures for studying quantum mechanics as a fresh starter? I tried r. Shankar but it only mathematical to me, couldn't get the physical significance. On the other hand, Griffith got way deep in concepts without sufficient examples...
  7. VonNathan

    I Could somebody tell me good book about degenerate matter ?

    Could somebody tell me good book about degenerate matter ?
  8. 1

    How is the Wave Function u(r) = Asin(kr) Normalized?

    Homework Statement I don't see how the author normalizes ##u(r)=Asin(kr)##. From Griffiths, Introduction to Quantum Mechanics, 2nd edition, page 141-142: http://imgur.com/a/bo8v6 Homework Equations ##\int_0^{\infty} \int_0^{\pi} \int_0^{2\pi}|A|^2 \sin^2(\frac{n\pi r}{a})r^2 \sin \theta...
  9. redtree

    A Conjugate variables in the Fourier and Legendre transforms

    In quantum mechanics, position ##\textbf{r}## and momentum ##\textbf{p}## are conjugate variables given their relationship via the Fourier transform. In transforming via the Legendre transform between Lagrangian and Hamiltonian mechanics, where ##f^*(\textbf{x}^*)=\sup[\langle \textbf{x}...
  10. A. Neumaier

    Insights The Vacuum Fluctuation Myth - Comments

    A. Neumaier submitted a new PF Insights post The Vacuum Fluctuation Myth Continue reading the Original PF Insights Post.
  11. TheSodesa

    The width of a finite potential well

    Homework Statement An electron is enclosed in a potential well, whose walls are ##V_0 = 8.0eV## high. If the energy of the ground state is ##E = 0.50eV##, approximate the width of the well. Answer: ##0.72nm## Homework Equations For an electron in a potential well, whose energy is less than...
  12. TheSodesa

    A relativistic electron in a potential box

    Homework Statement In a potential box (##L = 1.00pm##) an electron moves at a relativistic speed, meaning it's momentum can't be expressed as ##P = \sqrt{2mE}##. a) Using the uncertainty principle, show that the speed is indeed relativistic b) Derive an expression for the allowed energy states...
  13. J

    I Hartree Fock v.s. Configuration Interaction

    Hey everyone, For my studies I have to read a part about approximation methods in Quantum Mechanics. Unfortunately I'm having difficulties understanding some concepts. If I'm correct, for describing a multi fermionic system of n electrons, the Hartree Fock (HF) method uses a Slater determinant...
  14. M

    Setting up an Uncertainty Problem

    Homework Statement A proton is known to lie within the nucleus of a gold atom. The radius of a gold nucleus is approximately 6 fm. What is the minimum uncertainty in the proton’s velocity [you may treat the problem as one-dimensional and you should express your answer as a fraction of c]...
  15. P

    Momentum and Position Operator Commutator Levi Civita Form

    Homework Statement Prove that ##[L_i,x_j]=i\hbar \epsilon_{ijk}x_k \quad (i, j, k = 1, 2, 3)## where ##L_1=L_x##, ##L_2=L_y## and ##L_3=L_z## and ##x_1=x##, ##x_2=y## and ##x_3=z##. Homework Equations There aren't any given except those in the problem, however I assume we use...
  16. amjad-sh

    Studying Self-studying quantum mechanics

    Hello. I'm studying quantum mechanics by my own. I'm targeting to be a condensed matter physicist. What is the best way to grasp the concepts as fast as possible,and what should I do to become a good physicist in the near future? Thanks. Note: I've got a bachelor degree in physics but I stopped...
  17. weezy

    I Bohr-Sommerfield quantization of motion

    From wikipedia I understand that the old quantum condition $$\oint_{H(p,q)=E} p_i dq_i = n_i h $$ states that not all kinds of motion are permitted in a system. My question is why is this called the old quantum condition and what is quantization of motion? Does this mean that a particle jumps...
  18. A

    B Quantum field theory VS Quantum mechanics

    Hello I am little bit confused about one topic on theoretical Physics and that is If we want to describe our Quantum world (example atoms in metal) then should I use Quantum field theory or Quantum mechanics?
  19. G

    What Colors of Light Are Absorbed by Electrons in a 3.1 nm Infinite Well?

    Homework Statement Determine what colors of visible light would be absorbed by electrons in an infinite well, N = 3.1 nm. The effective mass for an electron in GaAs is one-fifteenth of the standard electron mass. Homework Equations En = πh2/[2*N2*me/15]*n2 L = nλ/2 Ψ = √(2/L)sin(nπx/L) The...
  20. I

    I Mass Defect: Exploring the Possibilities of Quantum Mechanics

    I've just watched a video by PBS spacetime on how an object with more potential energy has more mass, or less, in some cases (mass defect). But there is a problem. Quantum mechanics tells us that a particle has a chance of appearing at difderent places ( wave function), and that it also...
  21. J

    B Double Slit detectors question

    My question about the double slit experiment is this: why is it that nobody suspects that the detectors used to detect particles as they pass through the slits in the double slit experiment aren't causing some interference with the experiment which makes it seem as though they are acting like...
  22. TLeit

    Courses Quantum Mechanics Math Course

    Sorry I keep posting about this. I had settled on Probability (Probability in discrete and continuous sample spaces; conditional probability; counting techniques; probability functions; binomial, Poisson, normal distributions; and transformations of variables.) based off of previous answers to...
  23. K

    B Can quantum mechanics be derived from deeper principles?

    Can quantum mechanics be derived from deeper principles? For example, special relativity results directly from the fact that the speed of light is the same for all reference frames. Conservation laws of momentum and energy come from certain symmetries of space and time. Does quantum mechanics...
  24. RicardoMP

    I What is the width of a wave packet?

    I'm reading Gasiorowicz's Quantum Physics and at the beggining of chapter 2, SG introduces the concept of "wave packet" and gaussian functions associated to them. The first attached image is the 28th page of the book's 1st edition I suppose, and my question is about the paragraph inside the red...
  25. B

    Quantum "Modern Quantum Mechanics" by Sakurai for First Encounter

    Dear friends, Can "Modern Quantum Mechanics" by Sakurai be used as a first introduction to the quantum mechanics, given that I have a professor who can guide my reading and supplementary books? I recently got an opportunity for a reading course in rigorous QM, and I thought Sakurai would be a...
  26. RicardoMP

    I Square integrable wave functions vanishing at infinity

    Hi! For the probability interpretation of wave functions to work, the latter have to be square integrable and therefore, they vanish at infinity. I'm reading Gasiorowicz's Quantum Physics and, as you can see in the attached image of the page, he works his way to find the momentum operator. My...
  27. B

    Quantum mechanics: one thousand neutrons in an infinite well

    I apologize in advance for not being familiar with LaTex. 1. Homework Statement One thousand neutrons are in an infinite square well, with walls x=0 and x=L. The state of the particle at t=0 is : ψ(x,0)=Ax(x-L) How many particles are in the interval (0,L/2) at t=3? How many particles have...
  28. Automata-Theory

    A Particle Moving Along a Ring with Variable Potential

    Homework Statement Alrighty, so here's my problem in a nutshell: Some particle of mass m is confined to move along a ring of radius R. Since it's on a ring, it has periodic boundary conditions--i.e.: For the boundary defined as ##-\pi R \leq x \leq \pi R##, ## x = -\pi R ## and ## x = \pi R...
  29. C

    Programs Which is the best MSc programme (Condensed Matter Physics)?

    I'm a Physics student ending the bachelor degree in Physics. I'm strongly interested in Condensed Matter Physics (both theoretical and experimental), especially the quantum mechanical aspects that are linked to this field of studies. I'm trying to choose where to study for a MSc in Physics...
  30. A

    Quantum mechanics -- explanation of exothermic reactions

    Hi, I am wondering about latent heat release when water freezes but it seems best to start with a regular exothermic reaction. How does bond formation create heat? What is actually happening at the microscopic level so that these combining particles are capable of causing adjacent molecules...
  31. G

    Courses Quantum mechanics and astrophysics prerequirements

    Do i need to go through classical mechanics, electricity and magnetism, thermodynamics and some other physics courses to start studying topics like quantum mechanics, astrophysics, gravitation and relativity?
  32. J

    Hydrogen Atom: Wavefunction collapse after measurement of Lz

    Homework Statement Suppose we have a wavefunction with n=4. If we measure the orbital angular momentum along the z-direction(no spin in this problem) and get 2*hbar then what are the possible values of the total angular momentum and what is the most general wavefunction after the measurement...
  33. S

    Studying Advanced quantum mechanics in high-energy theory/cosmology

    I would like to know which chapters from the Advanced Quantum Mechanics textbook by Sakurai are most relevant to research work in high-energy theoretical physics. The kind of research topics that I have in mind pertain to work in string/brane cosmology, cosmological perturbations, dark matter...
  34. F

    Quantum Quantum Mechanics (Townsend or Mcintyre)

    I've heard good things about A Modern Approach to Quantum Mechanics by Townsend and Quantum Mechanics by Mcintyre. They use the same spin approach, but what are the pros and cons of each book?
  35. S

    A Utility of path integral formulation of quantum mechanics

    How does the path integral formulation of quantum mechanics as given by ##\langle q_{f}|e^{-iHt/\hbar}|q_{i}\rangle = \int \mathcal{D}q(t)\ e^{iS[q]/\hbar}## make manifest aspects of quantum mechanics such as symmetries?
  36. Q

    Quantum mechanics HW problem on infinite square well.

    1. ##<x>= \int_{0}^{a}x\left | \psi \right |^{2}dx## ##\psi (x)=\sqrt{\frac{2}{a}}\sin\frac{n\pi x}{a}## then ##<x>= \frac{2}{a} \int_{0}^{a}x \sin\frac{n\pi x}{a}dx## 2. Homework Equations 1) ##y=\frac{n\pi x}{a}## then ##dy=\frac{n\pi}{a}dx## and 2) ##y=\frac{n\pi x}{a}## then...
  37. Guilherme Vieira

    How to Calculate Probability using Density Operator?

    Hello, I'm trying to understand how to calculate de probability of finding a system in a specific eigenstate using the density operator. In the book of Balian, Haar, Gregg I've found a good definition of it being the expectation value of the projector Pr in the orientation of the eingenstate...
  38. resurgance2001

    I Equation Name & Description: What Is It?

    Could someone tell me what the attached equation is called, and just and brief description of what it states. I don't recognise it and it's hard to know where one goes to just look up an equation. Thanks
  39. Thomas Eaton

    B Virtual Particles; Making the Universe an Open System?

    The question here is simple; would the existence of virtual particles make the universe an open system? And if not, why? I thank all who consider this question for their time and would love to hear an answer.
  40. C

    I Are we in a simulation and quantum tunneling?

    Preface: As I understand it, according to quantum mechanics, there is a very good probability that I am sitting right in my chair right now, typing this question out. However, there is a non-zero, ever so small probability, however infinitesimally small chance that I am somewhere else in the...
  41. Tspirit

    A problem on calculus in Griffiths' book

    I can't understand the solution to Problem 1.4(a). The solution is the following: What puzzles me is that ρ(θ)dθ=ρ(x)dx ? Why are they equal?
  42. N

    B All the Universe belong to Quantum Mechanics?

    If we ever fully understood quantum science and all there is to know about it, could one say we then fully understand the universe? Or, would we never know at which point we know all there is to know? Would you be comfortable in the belief or proof nothing more could be discovered--about...
  43. INAM KHAN

    I Classical Mechanics v Quantum Mechanics

    I was thinking that what is solid reason behind the failure of Classical Mechanics in Black body radiation? Why classical mechanics not explain the curve at lower or higher range of frequncies.
  44. nickdi

    Compute Commutator: JxJy, Jz | i ħ Result

    Homework Statement Find the resul of [Jx Jy , Jz] where J is the angular momentum operator. Possible answers to this multiple chioce question are A) 0 B) i ħ Jz C) i ħ Jz Jx D) i ħ Jx Jz E) i ħ Jx Jy Homework Equations [AB,C]=A [B,C]+[A,B] B [Ji , Jj]=i ħ εijk Jk where εijk is the Levi-Civita...
  45. mertcan

    I Quantum mechanics getting position operator from momentum

    hi, initially I want to put into words that I looked up the link (http://physics.stackexchange.com/questions/86824/how-to-get-the-position-operator-in-the-momentum-representation-from-knowing-the), and I saw that $$\langle p|[\hat x,\hat p]|\psi \rangle = \langle p|\hat x\hat p|\psi \rangle -...
  46. K

    I About magnetic momentum in quantum mechanics

    Hi all, I have been reading lots of materials regarding the classical and quantum mechanics. The first subject I read is Bohr model, in which it is assumed the electron is in circular motion around the nucleus on the so-called orbital. I think it is semi-classical. With this assumption, we...
  47. sams

    I Hermitian operators in quantum mechanics

    Hello everyone, There's something I am not understanding in Hermitian operators. Could anyone explain why the momentum operator: px = -iħ∂/∂x is a Hermitian operator? Knowing that Hermitian operators is equal to their adjoints (A = A†), how come the complex conjugate of px (iħ∂/∂x) = px...
  48. K

    I About precessing directon of angular motion in quantum mechanics

    Hi all, I got a feeling that learning quantum mechanics is easy and hard. Most of time, it is easy to "accept" all the concepts given in the book by simply looking at their mathematical interpretation. But it is hard if you really take it serious to try to understand everything from the...
  49. J

    I What's the geometric interpretation of the trace of a matrix

    Hello, I was just wondering if there is a geometric interpretation of the trace in the same way that the determinant is the volume of the vectors that make up a parallelepiped. Thanks!
  50. F

    I Comparing Reduced Planck Masses

    What is the difference between these reduced Planck masses? ##M_p = \sqrt \frac{ħc}{8πG}~## and ##~M_p = \sqrt \frac{1}{8πG}## I see people use either, but what is the difference? It can't be that ħ and c are set to 1 because G is also a Planck unit and it would be nonsense to set a Planck...
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