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. J

    What Boundary Conditions Are Needed for Time-Dependent Hermitian Operators?

    Hello, could you please give me an insight on how to get through this proof involving operators? Proof: Given an eigenvalue-eigenvector equation, suppose that the vectorstate depends on an external parameter, e.g. time, and that over it acts an operator that is the fourth derivative w.r.t...
  2. K

    Scattering amplitude, link between quantum mechanics and QFT

    In quantum mechanics, we can define the scattering amplitude f_k(\theta) for two particles as the coefficients of an outgoing spherical wave. More precisely, the asymptotic behaviour (when r\rightarrow\infty) of a wave function of two scattering particles, interacting with some short range...
  3. F

    Good Books on Quantum Computing and Quantum Mechanics

    Hello guys, I will be starting my M.S Program in Solid State Electronics and was also curious about looking into quantum computing/superconductors. So can you guys suggest introductory levels books on quantum computing and and superconductors? I have an okay background in Physics (just...
  4. A

    Calculating Quantum Tunneling Probability - 1.524 eV, 343 pm, 2.654 eV

    Homework Statement What is the approximate transmission probability (in %) of an electron with total energy 1.524 eV through a barrier of thickness 343 pm, and a potential height of 2.654 eV? (Does it matter what the potential energy is before and after the barrier? Not really, as long as it is...
  5. J

    Books on quantum mechanics with intuition

    So, I know that there are a lot of questions about good books on quantum mechanics and I have read each one of them, and I go on and bought Griffiths' Introduction to Quantum Mechanics. But the fact is that it did not build me a very good intuition as it emphasized the computational part of it...
  6. M

    What is the difference between a vector and a vector space?

    What is the difference between a vector and a vector space? I get that a vector is an object with both magnitude and direction, but am confused by the term "vector space". Does a vector space simply refer to a collection of vectors? Thanks!
  7. S

    Different classical limits of quantum mechanics

    There is only one way to reduce the equations of special relativity (aka Lorentz Transformations) to the equations of Newtonian mechanics (aka Galilean Transformations). In light of the above, why are there multiple ways to reduce quantum-mechanical equations of motion into classical equations...
  8. 1

    Rewrite state in new basis - Quantum Mechanics

    Homework Statement Rewrite the state |ψ⟩ = √(1/2)(|0> + |1>) in the new basis. |3⟩ = √(1/3)|0⟩ + √(2/3)|1⟩ |4⟩ = √(2/3)|0⟩ − √(1/3)|1⟩ You may assume that |0⟩ and |1⟩ are orthonormal. Homework Equations The Attempt at a Solution [/B] I have a similar example in my notes however there...
  9. Aceix

    Quantum What are the best books that cover quantum mechanics

    Hi what are the recommended quantum mechanics books for a high school leaver. Also what are the math skills I need to know(book suggestions would help). Please I need to understand QM. I'm just interested!
  10. I

    Where Can I Begin Learning About Quantum Mechanics?

    I'm interested in quantum mechanics but I am not sure where to begin. I have a a good understanding of classical mechanics, but I don't know where to start in quantum mechanics. I seem to dive into subjects that are too complicated for me to understand at the moment. Where is a good starting...
  11. U

    Quantum Best textbook for learning quantum mechanics?

    I am looking for a textbook for learning quantum mechanics. So, i have never had a course in quantum mechanics(currently in a class called modern physics where they introduce us to modern physics topics, but no qm classes) So, I was looking for book for self learning. I might take graduate...
  12. C

    Taylor series expansion of an exponential generates Hermite

    Homework Statement "Show that the Hermite polynomials generated in the Taylor series expansion e(2ξt - t2) = ∑(Hn(ξ)/n!)tn (starting from n=0 to ∞) are the same as generated in 7.58*." 2. Homework Equations *7.58 is an equation in the book "Introductory Quantum Mechanics" by...
  13. S

    Photoelectric effect [was: Quantum Mechanics Questions]

    I'm currently self-studying quantum mechanics and instead of starting a new thread every time I have a new question I figure I'd just make one thread dedicated to all of them. I'm going over the Photoelectric Effect. The way I understand it is when light is shone on a metallic surface, the...
  14. Nate810

    Show that the expectation value of momentum is zero

    Homework Statement Demonstrate that the expectation value of momentum (p) for the wave function: ψ(x)∝e^(-γx) when x>0, ψ(x)=0 when x<0. Hint: Pay special attention to the discontinuity at x=0.[/B] Homework Equations <p>=<ψ|p|ψ>=∫dxψ*(x)[-iħ∂/∂x]ψ(x) from -∞ to ∞. [/B]The Attempt at a...
  15. K

    Show that the Slater Determinant states are a complete basis

    Homework Statement "Show that the Slater Determinant states are a complete basis" is the entire statement. Homework EquationsThe Attempt at a Solution I guess I'm trying to prove that the rank of the states is equal to the basis? I'm not sure where to start on this one.
  16. R

    Quantum Mechanics: Harmonic Oscillator

    Homework Statement A particle of mass m in the one-dimensional harmonic oscillator is in a state for which a measurement of the energy yields the values ##\hbar\omega/2## or ##3\hbar\omega/2## each with a probability of one-hald. The average value of the momentum ##\langle p_x\rangle## at...
  17. T

    Understanding General Relativity & Quantum Gravity

    Hello, I have a conceptual problem. How can both General Relativity and a theory of Quantum Gravity simultaneously exist? GR describes gravity as the curvature of spacetime, while QG is most likely a gauge theory. Furthermore, if gravity is indeed describedby particle interactions-what does...
  18. R

    Quantum Mechanics: Raising and Lowering Operators

    Homework Statement Consider a particle in an energy eigenstate ##|n\rangle.## Calculate ##\langle x\rangle## and ##\langle p_x\rangle## for this state. Homework Equations ##x = \sqrt{\frac{\hbar}{2m\omega}}(a+a^{\dagger})## The Attempt at a Solution ##\langle x\rangle =...
  19. Z

    Why Quantum Mechanics is Complex

    Why do Complex Numbers arise in Quantum Mechanics' computations? What kind of physical significance do they carry? Someone told me to read this paper: W E Baylis, J Hushilt, and Jiansu Wei, Why i?, American Journal of Physics 60 (1992), no. 9, 788–797. But I found it difficult for me to...
  20. P

    Basic Linear Alegbra for Quantum Mechanics

    I do not understand a work example in the book: ‘Quantum Mechanics DeMystified”. On page 212, part of Example 7-5: Given: Let { |a> |b> } be an orthonormal two-dimensional basis Let Operator A be given by: A = |a>< a |- i| a><b |+ i| b><a |- |b><b | Then: (The following part I do not...
  21. F

    The "Intelligence" behind quantum physics

    THE “INTELLIGENCE” BEHIND QUANTUM PHYSICS If the nature of quantum mechanics is that an observer affects the end “collapsed” state of a particle, than what constitutes a state of observation. The the only thing I can come up with that seems to determine what constitutes a form of observation is...
  22. lonely_nucleus

    Quantum Mechanics Required for Nuclear Engineering?

    I know that nuclear engineering requires some quantum mechanics but I want to know how much. Are there any textbooks that can fulfill the requirements for quantum mechanics in terms of nuclear engineering? I have heard of this book and I am a fan of old fashioned...
  23. MugiwaraNoSanji

    Quantum Quantum Mechanics and Quantum Chemistry books

    Hi, I've been self studying physics for a few years and I'm looking for some new books, specifically on Quantum Mechanics or Quantum Chemistry. It doesn't matter if they are PDF files or actual books, and price doesn't really matter. I've read Feynmans Lectures books and I'm looking for the next...
  24. N

    Why quantum mechanics looks so different from classical one?

    In many textbooks, the non-commutativity for the canonical pair is considered to lead to the major variaty from classical mechanism(CM) to quantum mechanism(QM), and change the Possion bracket into quantum commutator is a standard procedure called as canonical quantization. But in fact the...
  25. M

    How Does Light-Matter Interaction Challenge Classical and Quantum Views?

    I have just started reading about a classical electromagnetic treatment of light-matter interaction (beginning with dispersion relations, and then moving on to the standard phenomena - reflection, refraction, etc.). The discussion begins with a forewarning that light is not 'continuous' as the...
  26. R

    Quantum Mechanics: Wave Equation Probability

    Homework Statement Normalize the wave function $$ \langle x|\psi\rangle = \left\{ \begin{array}{l l} Ne^{-kx} & \quad x>0\\ Ne^{kx} & \quad x<0 \end{array} \right..$$ Determine the probability that a measurement of the momentum p finds the momentum between ##p## and ##p + dp## for this wave...
  27. T

    Where Am I Going Wrong in Sakurai's Quantum Spin Eigenvalue Problem?

    Homework Statement I am currently working on a seemingly straightforward eigenvalue problem appearing as problem 1.8 in Sakurai's Modern QM. He asks us to find an eigenket \vert\vec S\cdot\hat n;+\rangle with \vec S\cdot\hat n\vert\vec S\cdot\hat n;+\rangle = \frac\hbar 2\vert\vec S\cdot\hat...
  28. Z

    Relativity Books for relativity and quantum mechanics

    I have been looking online for books on introductory level quantum mechanics and General relativity that provide a mathematical introduction to these theories. Most of the books I have read until now provide a laymans introduction to these things. Since I'm only pursuing this as a hobby and...
  29. R

    Quantum Mechanics: Translation and Wave Function

    Homework Statement Let ##|\psi\rangle \to |\psi'\rangle = \hat{T}(\delta x)|\psi\rangle## for infinitesimal ##\delta x##. Show that ##\langle x \rangle = \langle x \rangle + \delta x## and ##\langle p_x \rangle = \langle p_x\rangle.## Homework Equations ##\hat{T}(\delta x) =...
  30. A

    What to Read/Study in Physics if I want to be a Physicict

    Hey I'm new to this forum and I'm 14 and I want to be a future Physicist (Probably Particle Physicist ) and I was wondering what books are good for starting out , just to let you know what kind of content I'm looking for I already know about General relativity , special relatativity , and the...
  31. C

    Quantum Mechanics is a set of Laws

    Hi, I know this is a basic question however, I am seeking absolute verification on these two points. 1) Quantum Mechanics is a set of Laws. 2) Laws only describe what we see. Theories give us the reason behind them.
  32. R

    Quantum Mechanics: Wave Mechanics in One Dimension

    Homework Statement Let ##\langle\psi| = \int^{\infty}_{-\infty}dx\langle\psi|x\rangle\langle x|.## How do I calculate ##\langle\psi|\psi\rangle?## Homework Equations ##\int^{\infty}_{-\infty}dxf(x)\delta(x-x_0)=f(x_0)## The Attempt at a Solution ##\langle\psi|\psi\rangle = \int\int...
  33. P

    Role of quantum mechanics in cosmology

    According to laplace,universe is totally deterministic.(one can tell position of object future position of object if he knows current position and velocity)but Heisenbergs's tells us that there is always uncertainty in position of particle and velocity.but Heisenberg's uncertainty only applies...
  34. Hamza Abbasi

    What is the value of A in Ψ=Acos^2(x) for a particle's wave function?

    Homework Statement The wave function of a certain particle is Ψ= A cos^2(x) for -π/2 < x < π/2. Find the value of A. Homework EquationsThe Attempt at a Solution My answer is coming out to be zero wheres as the correct answer is under root 8/3π ... Please help me out !
  35. J

    Requirements prior to Quantum Mechanics

    Hello! What are the requirements in physics and mathematics that somebody must have in order to start learning Quantum Mechanics by himself?
  36. B

    Exploring Quantum Mechanics & Time's Direction

    I have often heard that in quantum mechanics time has no direction. That the physics works the same going backwards in time than forwards. How does the wave function collapse of a particle follow this idea? If we could see time go backwards would we see particles turning back into waves? Is...
  37. T

    Stern Gerlach Spin 3/2, Quantum Mechanics

    Homework Statement [/B] Just trying to find the spin 3/2 rotation matrix, I've found spin 1/2 and spin 1. This isn't a homework problem just studying some other spins. Homework Equations For spin 1/2: Rn(Φ) = cos(Φ/2)1ˆ − isin(Φ/2)σn For spin 1: Un(Φ) = e −iΦSn = 1ˆ − isin(Φ) · Sn − (1ˆ −...
  38. B

    Quantum Mechanics, time independant solution in Dirac notati

    Homework Statement Consider the Hamiltonian: $$\hat{H}=C*(\vec{B} \cdot \vec{S})$$ where $C$ is a constant and the magnetic field is given by $$\vec{B} = (0,B,0) $$ and the spin is $$\vec{S} = (\hat{S}_{x},\hat{S}_{y},\hat{S}_{z}),$$ with$$\hat{S}_{x}...
  39. L

    Motion on a ring. Quantum mechanics.

    Homework Statement Particle of mass [tex[m[/tex] is confined on the ring of constant radius r_0. Solve Schroedinger equation for this problem. Homework EquationsThe Attempt at a Solution Problem is solved here http://www.physics.oregonstate.edu/~corinne/COURSES/ph426/notes3.pdf Why...
  40. Rimmonin

    Is there a space-independent Schrödinger equation?

    I'm learning about the Schrödinger equation in one of my uni courses, and we've recently gone past how to solve the time-independent version. That got me wondering if there is a space-independent version of the Schrödinger equation and what it could possibly be used for. I know I'm probably...
  41. M

    Operators in quantum mechanics

    Hi, We know the convergence of a series but what does it mean to say that "an operator converges or diverges"?
  42. T

    Reading list for learning Quantum Mechanics please

    Most probably, there was already a thread about this before, but I didn't find any with the search engine. Please, believe me, I tried a lot of words and found nothing like I'm going to ask now. I'm not a physicist...in fact, I'm a Political Sciences student with a great passion for Philosophy...
  43. S

    Quantum state of system before measurement

    Hello! If we consider a single-particle system, I understand that the measurement of an observable on this system will collapse the wave function of the system onto an eigenstate of the (observable) operator. Therefore, we know the state of the system immediately after the measurement. But as...
  44. R

    Matrix representation in x and y basis for spin operators

    Homework Statement How can I find the matrix representation of ##\mathbb{S}_+## and ##\mathbb{S}_-## in the ##|\pm y\rangle## or ##|\pm x\rangle## basis?Homework Equations ## \mathbb{\hat{S}}_+|s,m\rangle = \sqrt{s(s+1)-m(m+1)}\hbar|s,m+1\rangle ## The Attempt at a Solution The book almost...
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