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. dsatkas

    I Introduction to relativistic quantum mechanics and maybe QFT

    I'm aware that most modern textbooks gloss over relativistic qm and jump to qft. Since I'm not that brilliant of a student I'm thinking that i should firstly familiarize myself with relativistic and then go to qft. So my first question: Is it worth it to study relativistic qm or should i jump...
  2. T

    Two (almost) independent infinite square wells

    Homework Statement Consider a one-dimensional, nonrelativistic particle of mass m which can move in the three regions defined by points A, B, C, and D. The potential from A to B is zero; the potential from B to C is (10/m)(h/ΔL)2; and the potential from C to D is (1/10m)(h/ΔL)2. The distance...
  3. T

    Principal quantum number n is an integer, Why?

    Why is it necessary that the principal quantum number of a Hydrogen atom problem in Quantum mechanics must be an integer?Couldn't it be any fraction?
  4. hellsteiger

    What is the accepted interpretation of the quantum nature of matter?

    I'm having difficulty gauging what the accepted interpretation of the quantum nature of matter is. On the one hand I have been taught that properties of a particle are always definite, but due to the quantum nature of existence we cannot measure several properties to 100% accuracy at once. On...
  5. T

    Transform from Magnitude of P to R

    Hi everyone! How do I transform Momentum to Position in spherical coordinates?Thinker301
  6. DeathbyGreen

    Question of spin 1/2 particles in a rotating field

    Homework Statement So I'm given a spin 1/2 particle in a rotating magnetic field in the (x,y) direction and a constant field, B_0, in the z direction and am asked to find the S matrix describing it. Given is: B(t) = [B_1 \cos(\omega t), B_1 \sin(\omega t), B_0] Homework Equations H = \sum...
  7. fricke

    Quantum Mechanics (Bond distance)

    Homework Statement Two molecules of OCS (atomic weigh of S is 32 amu and the other one is 34 amu) have values of h/8π2I of 6081.490E6 [1/s] and 5932.816E6 [1/s], respectively. Calculate the C-O and C-S bond distance. (Note that I is moment of inertia) Homework Equations h/8π2I The Attempt at...
  8. I

    Eigenvalue of lowering operator

    How to prove that eigenvalue of lowering operator is zero?
  9. I

    Quantum Mechanics - Induction Method

    Let a be a lowering operator and a† be a raising operator. Prove that a((a†)^n) = n (a†)^(n-1) Professor suggested to use induction method with formula: ((a†)(a) + [a,a†]) (a†)^(n-1) But before start applying induction method, I would like to know where the given formula comes from. Someone...
  10. I

    Quantum Mechanics - Lowering Operator

    Homework Statement let A be a lowering operator. Homework Equations Show that A is a derivative respects to raising operator, A†, A=d/dA† The Attempt at a Solution I start by defining a function in term of A†, which is f(A†) and solve it using [A , f(A†)] but i get stuck after that. Can...
  11. V

    Do we need quantum mechanics to explain biological stuff?

    While I have to admit the question in its summarized version seems to be not very well defined (and naive, of an easy answer), so that I desire to at least make it sound less stupid. Or at least I hope. After reading all of this it might sound even worse though (no promises).I like reading about...
  12. Quandemonitum

    What is the wave function for the whole system/atom ?

    For example, let's say that psi(q) is the wave function of an electron(which describes/represents the electron) that is located in an atom and isolated/unentangled from the rest of the system. What is the wave function value of this psi(q) ? What is the wave function for that whole atom(with...
  13. Quandemonitum

    What is the wave function for the whole system/atom?

    For example let's say that psi(q) is the wave function of an electron(which describes/represent the electron) that is located in an atom and isolated/unentangled from the rest of the system. What is the wave function value of this psi(q) ?What is the wave function for that whole atom(with only...
  14. J

    Heisenberg Uncertainty Principle clarification

    I found these two examples in a books which demonstrate Heiseberg's uncertainty relation...
  15. AwesomeTrains

    Maximum position expectation value for 1D harmonic oscillator

    Hey, I'm stuck halfway through the solution it seems. I could use some tips on how to continue. 1. Homework Statement I have to determine a linear combination of the states |0\rangle, |1\rangle, of a one dimensional harmonic oscillator, so that the expectation value \langle x \rangle is a...
  16. T

    At what point should a grad student "understand" QM?

    Let me define the question better. For my purposes I'm saying a person "understand quantum mechanics" when they have what it takes to write a basic graduate level QM textbook. Maybe I'm setting the bar too high, but I'm a first-year physics grad student who can get good grades in QM classes...
  17. C

    Math for Modern Quantum Mechanics J.J. Sakurai

    Hi Guys, I am taking a quantum mechanics course next semester that follows Sakurai's book. I was wondering if there was some mathematics I should study over break in preparation for this course. I have taken so far: Calc 1-3 ODEs PDEs Linear Algebra An elementary course in group theory Ill...
  18. J

    Quantum Is Landau's book on QM suitable for undergraduates?

    Hello,i am just starting to learn Quantum Mechanics in the university at an underdrad level. I know there are a lot of great introductory books out there but i just saw that Landau's book on non-relativistic quantum mechanics has great reviews but upon seeing it,i was overwhelmed by the...
  19. A. Neumaier

    When are isomorphic Hilbert spaces physically different?

    In quantum mechanics, a Hilbert space always means (in mathematical terms) a Hilbert space together with a distinguished irreducible unitary representation of a given Lie algebra of preferred observables on a common dense domain. Two Hilbert spaces are considered (physically) different if this...
  20. T

    What are some good pedagogical QM papers?

    I did a search but couldn't find what I was looking for. I'm a physics student studying QM at the graduate level. I'm aware that "nobody truly understands QM" but I'd like to get as much insight and intuition as possible. Textbooks are good for learning to solve problems and learning the...
  21. KylieVegas

    Programs Masters in physics without a different bachelors degree?

    Hello I am an incoming Biology student (college), i really wanted to take applied physics as my course but my parents told me that it is better to be a doctor, anyways, it's summer here and I started taking Calculus 1 in coursera.com (i have NO backgroud in calculus because we don't have...
  22. M

    What exactly are interpretations of quantum mechanics?

    What exactly are interpretations of quantum mechanics? Is only one of them correct?
  23. N

    Quantum Mechanics and Group Theory questions

    Hello all. I am new here. I am in the last quarter of a 3 quarter sequence of undergrad quantum mechanics and I just had some conceptual questions (nothing pertaining to homework). We just recently covered Berry's Phase and the Dynamical Phase. Now I wanted to start with a more basic quantum...
  24. B

    Why do different objects have different colors?

    Why can we see colors? Everyone know that it is because of "reflected" light. But why is the light reflected? I've learned about abortion of light (excitation to higher quantum energy levels) and emission. But I don't know, why and how light is reflected. Please tell me why :-)
  25. micromass

    Math needed for quantum mechanics

    What math do I need to really understand quantum mechanics? Please advise! It might be too much, but since this is my new hobby: are there any cool books that combine quantum mechanics and biology?
  26. T

    How can you actually measure the electron position?

    Standard quantum mechanics text-books discusses Born rule, which states that the probability of finding a particle in a certain region in space is given by $$ |\Psi ({\bf r},t)|^2d^3r $$ Thing is, I never have seen a discussion about how you can actually measure the particle position in a...
  27. F

    Energy of the electron in a random hydrogen atom

    Does the energy of the electron in a random hydrogen atom is in superposition of all eigenvalues(some value upon measurement) or you will find it most likely in the ground state. Additional clarification: From my reading the textbooks said the electron energy is in superposition, yet the...
  28. J

    Proof on Operator Properties

    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...
  29. 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...
  30. 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...
  31. 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...
  32. 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...
  33. 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!
  34. 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...
  35. 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...
  36. 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!
  37. 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...
  38. 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...
  39. 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...
  40. 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...
  41. 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...
  42. 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.
  43. 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...
  44. 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...
  45. 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 =...
  46. 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...
  47. 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...
  48. 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...
  49. 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...
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