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. 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...
  2. 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...
  3. 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...
  4. N

    Are These Spectroscopic Notations Physically Possible?

    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...
  5. 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 -...
  6. 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?
  7. 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...
  8. 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...
  9. 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...
  10. 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...
  11. 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
  12. 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 $r$...
  13. 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...
  14. 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...
  15. 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...
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. 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...
  21. 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."...
  22. 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...
  23. D

    Boundary conditions for a step potential

    Homework Statement A particle with mass m and spin 1/2, it is subject in a spherical potencial step with height ##V_0##. What is the boundary conditions for this eigenfunctions? Find the degeneracy level for the energy, when it is ##E<V_0## Homework Equations Radial equation \begin{equation}...
  24. Z

    Studying Is it possible to understand quantum mechanics in student life?

    QM is gradually conquering my mind day by day. i can't think anything expect it. i always thinking while eating,before sleeping,in classroom,while outside. my college performence is badly affecting as QM is not in my course. i just want to understand anyhow_could anybody guides me to understand it.
  25. ohwilleke

    I Do these equations have a non-trivial solution?

    I was reading the following article that tries to use some equations originally proposed by Pauli in 1951 to reason from one of two reasonably plausible axions that there are tight constraints on the fundamental particle content and mass spectrum of the Standard Model together with BSM...
  26. Urs Schreiber

    Insights Introduction to Perturbative Quantum Field Theory - Comments

    Urs Schreiber submitted a new PF Insights post Introduction to Perturbative Quantum Field Theory Continue reading the Original PF Insights Post.
  27. A

    I Principle of superposition of states

    Upon reading Landau QM, the Principle of superposition of states, I got confused. It states (and i quote): "Suppose that, in a state with wave function Ψ1(q), some measurement leads with certainty to a definite result 1, while in a state with Ψ2(q) it leads to a different result 2. Then it is...
  28. C

    Quantum mechanics transitions in an electromagnetic field

    Homework Statement This is problem (7.1) from John A. Peacock "Cosmological Physics". Show that the first-order perturbation term for quantum mechanics with an electromagnetic field, ##(e/m) \mathbf{A \cdot p}## is proportional to the electric dipole moment. What is the interpretation of the...
  29. S

    Programs Applied Physics specialization: Biophysics vs Quantum

    Hi! I am starting my Master's in Applied Physics at the TU Delft next week and I have yet to decide a research track (i.e. specialization). I have narrowed my options down to bionanoscience and quantum nanoscience. Of these two, which would be better? Of course, 'better' is a vague term, so what...
  30. S

    I Applying the Principle of Relativity to Quantum Mechanics

    I read the forum rules, I hope I am not breaking them as these principle is generally accepted and I am not contradicting mainstream science. "The principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer...
  31. W

    Quantum Mechanics: Expectation values (Griffiths)

    Homework Statement A few questions: Q1) How does 1.29 flow to 1.30 and 1.31? How was the integral-by-parts done? Q2) The author states that <v> = d<x>/dt represents the expectation value of velocity. What does this actually mean? I tried to rationalise that d<x>/dt represented the velocity...
  32. Demystifier

    Insights How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics - Comments

    Demystifier submitted a new PF Insights post How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics Continue reading the Original PF Insights Post.
  33. T

    I New book on the foundations of quantum mechanics

    Some years ago now, I was a regular reader and poster here and had a lot of fun arguing about the meaning of Bell's theorem, the relative merits of different "interpretations" of QM, etc. I just popped in for the first time in a long time, and it is nice to see some familiar faces (and many new...
  34. P

    Quantum Quantum Mechanics Textbook,Zettili vs Shankar

    Hello Everyone, I am an undergraduate physics student who planned to study quantum mechanics. I have been reading the introductory book by Griffiths, however I found that his book seldom uses Dirac Notation and there is little about mathematical formalism on quantum mechanics. Therefore I would...
  35. M

    I Compatibility of Quantum Mechanics and Special Relativity

    Hello, In my free time, I've been learning about an eclectic range of topics (ie. French History, Kinetic Theory etc.). Most recently I've been focused on Quantum Mechanics, which happens to be most complex topic I've ever looked at. Typically I write up summaries after reading from various...
  36. T

    I Relativistic Quantum Mechanics vs Quantum Field Theory

    What's the difference between relativistic quantum mechanics and quantum field theory? In principle, my guess is that to do the former, one needs to express the Hamiltonian in a relativistic, Lorentz invariant, form, because it seems to be the only frame-related term in the wave equation. (Is...
  37. D

    Constants of motion in quantum mechanics

    Homework Statement A particle of mass m and spin s, it's subject at next central potential: ## \begin{equation*} V(\mathbf{r})= \begin{cases} 0\text{ r<a}\\ V_0\text{ a<r<b}\\ 0\text{ r>b} \end{cases} \end{equation*} ## Find the constants of motion of the system and the set of...
  38. D

    A Asymmetry parameter while relating proper time with distance

    In special relativity, we know, (proper time)^{2} = - (proper distance)^{2}. But, in Causal Dynamical Triangulations (CDT), they introduce an asymmetry parameter \alpha as, (proper time)^{2} = - \alpha (proper distance)^{2} [Q. 1] Can you please explain me about, why we need to introduce \alpha...
  39. F

    I Angular dependance of NEXAFS spectroscopy - derivation

    Hi all, this is my first time posting so I hope it's in the right place, if not I apologise. I'm trying to understand the angular dependence in NEXAFS spectroscopy for linearly polarised light. So from what I understand, the quantum mechanical description of the excitation process for a single...
  40. W

    Quantum Mechanics: Outside a (in)Finite Well

    Homework Statement Referencing image attached. I'm not sure how the example arrived at ψ ⇒ 0 at x<0 and >L as K ⇒ ∞ in the limiting case of an infinite potential well. Homework EquationsThe Attempt at a Solution I tried simply applying limits to the wavefuction but in the case x<0, the...
  41. tomdodd4598

    I 'Normalisation' of Fourier Transforms in QFT

    Hi there - just a quick question about Fourier transforms: When learning about quantum mechanics, I found that the Fourier transform and inverse Fourier transform were both defined with constants of ##{ \left( 2\pi \right) }^{ -d/2 }## in front of the integral. This is useful, as...
  42. O

    Time independent Schrödinger Eqn in a harmonic potential

    Homework Statement I am currently reading a textbook on solving the Schrödinger equation for the harmonic oscillator using the series method; $$-\frac{\hbar^{2}}{2m}\frac{\mathrm{d}^2 \psi }{\mathrm{d} x^2}+\frac{1}{2}m\omega ^{2}x^2\psi =E\psi $$ It starts by using these two dimensionless...
  43. C

    I How do we interpret an EM wave using Quantum Mechanics?

    I know that if the intensity of a light beam with of a certain frequency varies it means the number of photons the light beam is composed of varies and not the individual photons energy. That would mean the E and B field amplitudes vary. This would mean that that the amplitudes of the E and B...
  44. C

    I Deductions of Formulas for Energy

    So, I am a newbie in quantum mechanics, took modern physics last fall for my physics minor. I know that Schrodinger based his equation based on the equation K + V = E, by using non-relativistic kinematic energy (P2/2m + V = E) p becoming the operator p= -iħ∇ for the wave equation eigenfunction...
  45. RJLiberator

    Quantum Difference between these two Griffiths Quantum Mechanics books

    1. Amazon link: https://www.amazon.com/dp/0131118927/?tag=pfamazon01-20 ISBN: 978-0131118928 This is the book that my class syllabus suggests based off ISBN number, however it is $119.00 to buy off Amazon. 2. Amazon Link: https://www.amazon.com/dp/1107179866/?tag=pfamazon01-20 ISBN...
  46. M

    A How can quantum mechanics contribute in a Nuclear reactor

    Hi, does treating neutrons as waves make any difference when it comes to micro cross sections ? , does quantum mechanics help more than classical mechanics in nuclear reactor physics ? Noticing that I am a nuclear engineering student
  47. binbagsss

    Quantum mechanics Hermitian operator

    Homework Statement I have the criteria: ## <p'| L_{n} |p>=0 ##,for all ##n \in Z ## ##L## some operator and ## |p> ##, ## |p'> ##some different physical states I want to show that given ## L^{+}=L_{-n} ## this criteria reduces to only needing to show that: ##L_n |p>=0 ## for ##n>0 ##...
  48. noir1993

    Quantum Thoughts on Sakurai's Quantum Mechanics textbook

    I have taken a couple of graduate level courses in quantum mechanics and I have decided to read Sakurai's Modern Quantum Mechanics from cover to cover, partly because I liked his style and I have heard a lot of people talk highly of it. But I recently realized that the second edition of the same...
  49. Jianphys17

    Quantum Math Methods for Quantum Mechanics (QM) Prerequisites

    Hi, people I wondered if as prerequisites for QM, the Kreyszig (for func. analysis) and Hassani's book they be suffices .. Thank you in advance !
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