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.

View More On Wikipedia.org
  1. J

    Sources to learn about Berry phases and Adiabatic Theorem

    Hello, I recently went through Griffiths' Quantum Mechanics text and there is a chapter called the Adiabatic Theorem that includes Berry phase and the Aharonov-Bohm effect. As I found them very interesting, I would appreciate if anyone could provide me with some good sources(books, internet...
  2. J

    Quantum Problems books in various topics in Physics

    I want college-level problems books on the following physics topics: 1)Quantum Mechanics 2)Electromagnetism 3)Classical Mechanics 4)Thermodynamics (and Statistical Mechanics) 5)Waves 6)Special Relativity
  3. N

    No interference pattern in double slit when there is a lens?

    Why does the interference pattern of the photon go away when one places a convex lens far away from the two slit to only show a particle build up of the two slits? This is the experimental set up, the lens is in place far after the photons pass through the two slit and hit the back wall in a...
  4. M

    Quantum mechanics exam (want to solve by myself)

    Hi i am studying for an exam (after failing the first one) on Quantum mechanics that is in one month from now. I use the lecture notes from the teacher. It includes the following topics and 25 exercises per chapter: Formalism of classical physics state vectors and operators position and...
  5. M

    Why electrons never make contact with the nucleus?

    Hi everyone: This concept has bothered me for a while. The concept being that two oppositely charged particles (electron and proton) are attracted to each other, but the electrons go on a orbital trajectory around the nucleus instead of directly "sticking to" the nucleus. The closest I have...
  6. G

    Literature for QM to QFT step-by-step

    Hi all, can anybody help me to find literature that takes the reader on a step-by-step path from non-relativistic quantum theory to relativistic quantum theory? I imagine something like that: it starts with a single harmonic oscillator, analyzes the non-harmonic oscillator (does the...
  7. Noctisdark

    Is Quantum Mechanics an artifact of our ignorance?

    I've read a lot about QM and studied the math and how it work many and many times in several lectures in several places, but whenever I review what the theory says and compare it to how the measurement work, I come to doubt in the theory it self, I think it can even be explained using classical...
  8. PhysicsKid0123

    I need advice on upcoming course schedule

    So I really have a few questions. First, is it wise to take the following classes in the same semester? Quantum Mechanics I - At the level of Griffiths' Intro to Quantum Mechanics, chapters 1-5ish Classical Dynamics - At the level of Thorton and Marion, Chapters 1-12, ends with coupled...
  9. D

    Exploring the Mystery of Blank Spaces in Quantum Mechanics

    So, I am kind of learning QM on my own, and through my chemistry book. It doesn't explain any further than the shapes of orbitals, and I am wondering did anyone found out why is space in the orbitals between the clusters of probability blank.
  10. A

    Mathematics of Quantum Mechanics

    I have a question about learning the mathematics of Quantum Physics... So, I've been really interested in Astronomy and Quantum Physics since I was a kid. Owing to some accidental education and career choices, I however, ended up becoming a Business Consultant. Although I have spend most of my...
  11. 95Tesla

    Is my Fall Schedule too Difficult?

    I'll be starting my junior year this coming fall, and I want to know what people think about my intended schedule. Quantum Mechanics I (3 cr.) Intermediate Electricity and Magnetism (3 cr.) Wave Motion and Optics Lab with Writing (4 cr.) Numerical Mathematical Analysis (3 cr.) Exploration...
  12. M

    Programs Which degree for quantum mechanics?

    I am currently 16, and will finish my middle school (hopefully!) in two years. I'll have to choose a university and a degree soon, and I have a few doubts. First of all, is it possible to do my bachelor in the Netherlands and my master in another country like, say, the UK? Second of all, do any...
  13. N

    What is a universal wavefunction in MWI?

    I'm alittle confused, is it saying that all the fundamental particles in the universe are really just one wave function?
  14. N

    Can string theory and Penrose interpretation coexist?

    Can the M theory/ string theory coexist with the penrose interpretation of quantum mechanics?
  15. N

    Understanding STM Microscopes: The Role of Voltage in Physics

    when physicists say that they apply voltage to the tip or the sample, do they mean that the tip or sample become electrically charged?
  16. T

    How to explain the term quantum mechanics in 10 minutes?

    How to explain the term quantum mechanics to a class in 10 minutes? I may need to do this in an oral exam where the professors are from English department. Whiteboard can be used. My presentation should include one or more of the following:· Examples (practical and/or personal)·...
  17. Cobalt101

    Delayed choice measurement subsequent analysis

    This is a variant associated with the Scully and Druhl signal-idler photon delayed choice experiment, as described and discussed in Brian Greene's Fabric of the Cosmos. The commentary notes the "delay" may be configured to happen a very (years) long time after the photons pass the two...
  18. quantumfunction

    How different can quantum vacuums be?

    For instance our quantum vacuum has a certain Cosmological constant and the question is can there be other vacuums with different values and if so where's the evidence for this I would like to read it. How do you derive the Cosmological Constant through something like Quantum field theory or...
  19. fricke

    Particle in a box with the finite depth

    For particle in a box with the finite depth, is it traveling wave? or standing wave? I am confused with its ability to pass through the potential walls that is classically forbidden area which makes me think it is traveling wave. But for particle in a box with infinite potential, I understand...
  20. fricke

    Do momentum and kinetic energy operators always commute for a free particle?

    For particle in the box wave function, it is the eigenfunction of kinetic energy operator but not the eigenfunction of momentum operator. So, do these two operators commute? (or it has nothing to do with commutator stuff?) How about for free particle? For free particle, the wave function is...
  21. K

    Exact solutions for potential V=(|x|-a)^2

    I heard that this potential is exactly solvable (ie one can find the eigenstates of the quantum mechanical problem exactly). However, I can not find a reference. I heard it is in Merzbacher, but I can not find it. Is it correct that this is exactly solvable? Can someone provide a good reference?
  22. G

    Why Study QM and Electrodynamics for Materials Science?

    Decided to make this account in order to supplement my studies of QM by Griffiths and Electrodynamics by Jackson. I'm finishing my BS in chemical engineering soon and then it's onto grad school to study materials science :).
  23. 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...
  24. 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...
  25. 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?
  26. 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...
  27. T

    Transform from Magnitude of P to R

    Hi everyone! How do I transform Momentum to Position in spherical coordinates?Thinker301
  28. 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...
  29. fricke

    How to Calculate Bond Distance in OCS Molecules?

    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...
  30. I

    Eigenvalue of lowering operator

    How to prove that eigenvalue of lowering operator is zero?
  31. 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...
  32. 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...
  33. 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...
  34. 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...
  35. 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...
  36. J

    Heisenberg Uncertainty Principle clarification

    I found these two examples in a books which demonstrate Heiseberg's uncertainty relation...
  37. 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...
  38. 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...
  39. 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...
  40. 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...
  41. 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...
  42. 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...
  43. 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...
  44. M

    What exactly are interpretations of quantum mechanics?

    What exactly are interpretations of quantum mechanics? Is only one of them correct?
  45. 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...
  46. 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 :-)
  47. 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?
  48. 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...
  49. 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...
Back
Top