What is Quantum numbers: Definition and 122 Discussions

In chemistry and quantum physics, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be known with precision at the same time as the system's energy—and their corresponding eigenspaces. Together, a specification of all of the quantum numbers of a quantum system fully characterize a basis state of the system, and can in principle be measured together.
An important aspect of quantum mechanics is the quantization of many observable quantities of interest. In particular, this leads to quantum numbers that take values in discrete sets of integers or half-integers; although they could approach infinity in some cases. This distinguishes quantum mechanics from classical mechanics where the values that characterize the system such as mass, charge, or momentum, all range continuously. Quantum numbers often describe specifically the energy levels of electrons in atoms, but other possibilities include angular momentum, spin, etc. An important family is flavour quantum numbers – internal quantum numbers which determine the type of a particle and its interactions with other particles through the fundamental forces. Any quantum system can have one or more quantum numbers; it is thus difficult to list all possible quantum numbers.

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  1. S

    How many combinations are possible with the four quantum numbers?

    1. how many combinations are possible with the four quantum numbers? 2. Does Pauli's exclusion principle apply only to electrons within the same atom? can it apply across atoms as well? how is the exclusion principle generalized across atoms?
  2. X

    Representation of quantum numbers +1/2 and -1/2

    Homework Statement The quantum numbers +1/2 and -1/2 for the electron spin represents? Homework Equations a) rotation of electron in clockwise and anticlockwise directions respectively b) tow quantum mechanical spin states which have no classical analogue c) Magnetic moment of electron...
  3. A

    Question About Quantum Numbers

    I have a question about a specific passage in Hill's book on statistical thermodynamics. I have decided to teach myself the subject, but with having taken any classes in modern physics sometimes I encounter foundational material that I have no experience with. This question should be pretty...
  4. X

    Quantum numbers (free particles)

    Do free particles have quantum numbers? What are they?
  5. V

    Question about quantum numbers:

    So, you got n,l,m_l,m_s. If you have two hydrogen atoms on opposite ends of the universe, it seems to me that the electron in each could have the set of quantum numbers (1,0,0,1/2). Now, if you have a helium atom, because its two electrons are identical fermions, by the PEP they now "know"...
  6. H

    Correct quantum numbers interpretation?

    Greetings everyone, I'm going through Griffiths QM, and just wanted to make sure I understood the roles (where they come from, etc.) of the quantum numbers n, l, and m. What is written below is basically an outline of my current understanding, of which I am seeking either a confirmation or...
  7. K

    Unlocking Quantum Numbers for Lithium Atom

    Homework Statement Lithium has an atomic number Z = 3. Two of its electrons have the quantum numbers {n, L, m{l}, m{s}} = {1,0,0,+1/2} and {1,0,0,-1/2}. Write down the corresponding set of quantum numbers for the third electron in the lowest energy state of the Li atom. Briefly explain the...
  8. nukeman

    Help: Question about Orbitals and Quantum numbers - Thanks

    Homework Statement Assume that you travel through space to a strange universe where the allowable values for the quantum numbers are quite different from those in our own universe. In this new universe, s orbitals may contain a total of 2 electrons, p orbitals may contain a total of 4...
  9. nukeman

    Help: Writing the 4 quantum numbers for each of the 8 electrons?

    Homework Statement An oxygen atom has a total of 8 electrons. Write the four quantum numbers for the each of the eight electrons in the ground state? I can't seem to figure this out. I know this... O = 1s^2 2s^2 2p^4 But from that, I don't know how to finish the question...
  10. R

    Which set of quantum numbers is not possible

    Which set of quantum numbers is not possible? a. N = 5, l =3 , ml = 0 , ms = -1/2 b. N = 1, l = 0, ml = 0 , ms = 1/2 c. N = 3 ,l = 2, ml = 1, ms = 1/2 d. N = 4, l = 3, ml = -3, ms = 1/2 e. N = 5, l = 2, ml = 0, ms = -1/2 They all look possible to me and there is no none of the above...
  11. M

    Quantum numbers related to every flavour of quark

    Hi. I am a bit confused by the fact that there are quantum numbers related to every flavour of quark except the up and down. A consequence of this is that the neutral pion is it's own anti-particle while the neutral kaon is not. Why is this so?
  12. C

    Why are there not up and down quantum numbers?

    Hi. I am a bit confused by the fact that there are quantum numbers related to every flavour of quark except the up and down. A consequence of this is that the neutral pion is it's own anti-particle while the neutral kaon is not. Why is this so?
  13. G

    Writing 4 Quantum Numbers for Electron in 3D Orbital

    what are the different ways to write four quantum numbers that designate an electron in a 3d orbital
  14. fluidistic

    Modern physics, quantum numbers, subshells

    Homework Statement Find all the terms of an atom whose last subshell is np³.Homework Equations M_L=\sum _i m_{l _i} M_S=\sum _i m_{s _i} The Attempt at a Solution My professor did the same exercise but with np². Basically he wrotes all the possible quantum numbers for the atom: 1)m_l=1...
  15. A

    How Many Quantum Numbers Define a Spin 1/2 Particle's State?

    this sounds like a question that should be answered somewhere, but i can't find it. how many quantum numbers does it take to specify the state of a spin 1/2? 1. if it points along z, then just 1: the eigenvalue of Sz will do (up to global phase) A. whether or not in a B field B. if...
  16. L

    Angular momentum quantum numbers and spectroscopic notation

    Homework Statement find each of the angular momentum quantum numbers and the spectroscopic notation of the ground state electron configuration. Homework Equations n2s+1L J The Attempt at a Solution so for "each of the angular momentum quantum numbers" I am just finding the L in...
  17. fluidistic

    Quantum numbers in wikipedia's table

    I don't understand why there are 2 dashed values in this table: http://en.wikipedia.org/wiki/Quantum_number#Quantum_numbers_with_spin-orbit_interaction. I have that j=l+s,l+s-1,...,|l-s|. So let's take #1 of the table. They give l=1 and we know that s=1/2. Thus j=l+s=3/2 or j=l-s=1/2. Why...
  18. fluidistic

    Electrons and their quantum numbers for the oxygen atom

    Homework Statement Write down the electonic configuration for the O atom. Write down the quantum numbers (n,l,m_l,m_s) for each one of the electrons. Homework Equations Pauli exclusion principle. Least energy principle for filling the shells. The Attempt at a Solution...
  19. fluidistic

    Possible Quantum Number Combinations for 2p State

    Homework Statement List all possible values for the quantum numbers n, l, m_l and m_s for a state 2p. If an atom has 2 electrons 2p, how many states are there?Homework Equations Simple ones.The Attempt at a Solution n=2. l=1. m_l=-1, 0, 1. m_s=-1/2, 1/2. Now I'm confused on how to answer the...
  20. fluidistic

    Understand some quantum numbers in a problem

    Homework Statement Consider the following states of the hydrogen atom corresponding to l=2 whose quantum numbers corresponding to L_z and S_z are given by m_l=2, m_s=-1/2 and m_l=1, m_s=1/2. What are the possible values for the quantum number j for the states m_j=3/2? Homework Equations...
  21. K

    Eigenvaules and quantum numbers

    Eigenvalues and quantum numbers My professor was discussing the Schrodinger equation in 3-d today and mentioned that there are degeneracies within quantum numbers (for the hydrogen atom, the x, y, and z components are symmetric?). Does that imply that the eigenvalues of some operator are the...
  22. teroenza

    Electron in a 1-D box. Quantum Numbers

    Homework Statement Imaging an electron (s=1/2) confined in a one-dimensional rigid box/ What are the degeneracies of its energy levels? Make a sketch of the lowest few levels, showing their occupancy for the lowest state of six electrons confined in the same box. (Ignore the Coulumb...
  23. T

    How to determnine quantum numbers of hybridized orbitals?For

    How to determnine quantum numbers of hybridized orbitals? For example:We have sp3 orbital,so its quantum numbers are n=1,l=0 and 1,m=0 and -1,0,1?Or how?Or they are in some way added up together? Thanks
  24. B

    Question about angular momentum quantum numbers

    This is just a short question about angular momentum quantum numbers, not a homework problem. So in my textbook it states that the letters s,p,d,f correspond to the angular momentum quantum numbers 0,1,2,3 respectively. But what if l = 5? Then what letter to use? The book does say that n...
  25. G

    Quantum Numbers for Electron Spin

    Hi afaik S² does commute with an arbitrary component of the Spin, so this should give 2 quantum numbers, but they always say that there is just this 1/2 and -1/2 for the hydrogen atom. So my question is: Why is there only one quantum number to characterize the spin of an electron?
  26. M

    Cant understand similar proof Quantum numbers from PDE (pdf attachment)

    I believe that this is similar to the proof of schrodinger equation to obtain quantum numbers, however i cannot seem to understand the relationship between n, l and m: I have attached a pdf file on partial differential equations and on page 5, i cannot seem to understand why it is +n^2 and...
  27. Z

    Angular-Momentum Quantum Numbers

    Is there any generally accepted or even speculative a priori reason why the orbital-angular-momentum quantum number is allowed to take on only integer values but the spin-angular-momentum quantum number may have half-integer values, or is this just empirical?
  28. B

    The Zeeman Effect: Determining Atomic Level Quantum Numbers

    Homework Statement Explain why the Zeeman effect can assist in the determination of the quantum numbers of atomic levels Homework Equations The Attempt at a Solution Not sure why this is I understand what the Zeeman effect is, and the source of the splitting on energy...
  29. N

    Quantum numbers of atoms in a given state (number^number)letter

    Quantum numbers of atoms in a given state "(number^number)letter" Homework Statement An atom is in the state 42F. Write down the values of n,l,s and j. Homework Equations The Attempt at a Solution n=4 l=3 I'm having problems with s and j. I know j=l+s, does one...
  30. K

    Angular momentum quantum numbers

    Homework Statement Remembering that a bound state exists if the effective potential is negative, find an angular momentum quantum number l0 such taht for all l<l0 the states are bound. The given potential is V=(C/r3)-(D/r2), where C and D are positive numbers. Homework Equations...
  31. B

    Quantum Numbers for Hydrogen Atom Electron

    Homework Statement Define the quantum numbers required to specify the state of an electron in hydrogen. The spatial part of the wave-function describing a particular hydrogen atom has no angular dependence. Give the values of all the angular momentum quantum numbers for the electron...
  32. N

    Selection rules and quantum numbers

    Homework Statement From past paper: State the selection rules for (electric) quantum numbers n,l,m,s and j. Homework Equations The Attempt at a Solution My problem is that looking online, there seems to be an m(s) and m(l). Is the question assuming that I state the selectrion...
  33. Physics Monkey

    Baryon quantum numbers from partons

    Hi everyone, I have a perhaps slightly vague question for all the QCD experts out there. The simplest description of hadron quantum numbers comes from the parton picture where I attempt to simply add up the quantum numbers of a few partons that are supposed to make up the hadron. However, in...
  34. U

    How many quantum numbers would the system have overall?

    If the angular momenta about three axes of rotation in a central potential did commute, how many quantum numbers would the system have overall?
  35. N

    Questions on Quantum Numbers (introductory physics)

    Hello, I'm taking a course in introductory modern physics, and I have a few questions on the nature of quantum numbers: Why is \Delta l = \pm 1? My book simply states this is due the angular momentum of photons, but we have that L_{photon} = \pm 1 \hbar and L_{electron} = \sqrt{l(l+1)} \hbar...
  36. B

    Quantum Numbers j,J: Values & Possibility of 0

    Homework Statement which values can the quantum numbers j and J take on, can they take on the value 0? Homework Equations The Attempt at a Solution j=l+s and both l and s can be 0 so j can become zero, am I right?
  37. G

    Exploring the Relation of Quantum Numbers

    hey, i asked myself, how one could derive the relations for the quantum numbers... so why is: l always: 0<l<n-1 from what follows this relation for l does anyone know this?
  38. R

    Are all of the quantum numbers of anti-particles opposite

    Hey Just wondering- Are all of the quantum numbers of anti-particles opposite to their corresponding particle quantum numbers? I know that lepton numbers are opposite for particles and anti particles As is charge... But what about the quantum numbers like strangeness, spin, parity...
  39. A

    Radial probability density / quantum numbers.

    In my notes for a module on atomic and molecular physics it has this statement: "For a given n the probability density of finding e- near the nucleus decreases as l increases, because the centrifugal barrier pushes the e- out. So the low-l orbitals are called penetrating." I just want to...
  40. I

    Physical observables determined by quantum numbers: n, l, ml, ms

    exam practise question: what are the physical observables determined by the quantum numbers n, l, ml and ms of the electron in a hydrogen atom. most places just give the equation or the name not the physical observable determined. so is this right?:- n = principal number determines the...
  41. K

    Quantum Numbers and Total number of Orbitals

    Homework Statement How many orbitals have the values n = 4, l = 3, and m_l = -2? Homework Equations First of all, is this question asking me how many orbitals there are with the given quantum numbers? Second, how do I go about finding that out The Attempt at a Solution I thought...
  42. F

    Quantum Numbers J,S and L in p+n and n+n system

    Hey, I have some problems concerning one of the exercises I got last week Homework Statement List the quantum numbers J,S,L (in spectroscopic notation ^{2S+1}L_J for partial waves of the n + p systemup to total angular momentum J=2 The quantum numbers J, S and L represent the total...
  43. S

    How are quantum numbers used to classify eigenvectors of a Hamiltonian?

    What exactly are quantum numbers? I read the Wikipedia page on them but it is just way to complicated for me.
  44. J

    Atomic terms and quantum numbers?

    Hi, I have a helium atom in the excited state of (1s,20p), and I am told that it has 4 corresponding atomic terms. I am supposed to "write down the quantum numbers of these 4 atomic terms". As I understand it, an atomic term is specified by the 2S+1LJ notation, where S is the spin quantum...
  45. K

    Quantum numbers of a field acquiring vacuum expectation value

    Why should symmetries require a field that acquires vacuum expectation value to have the same quantum numbers as the vacuum? Please give me a reference also..if possible...
  46. M

    Demystifying Quantum Numbers: Understanding the Role of n, l, and ml

    I am still totally confused about the principle quantum number even though i got passed the unit with a A+ on the exam. does the principal quantum number, n, have anything to do with the period? Does the "n" value, which leads to the "l" and "ml" actually indicate all the possible orbitals for a...
  47. H

    Quantum numbers of N/Deltas resonances

    I've been working on something and I seem to have hit a noose. The PDG lists many N/Delta resonances, but let's focus on four of them, each with JP=3/2+: *N(1720), P13, http://pdg.lbl.gov/2009/listings/rpp2009-list-N-1720-P13.pdf *Delta(1232), P33...
  48. A

    The Hydrogen Atom: An Unique Case of Quantum Numbers

    Why is the hydrogen the only atom that depends only on principal quantum number n and for all other elements, energies depend on both orbital quantum number and principal quantum number?
  49. C

    Angular momentum quantum numbers

    Homework Statement What are the allowed values of the total angular momentum quantum number j for a particle with spin s=3/2 and orbital angular momentum quantum number l=2? I know that the angular momentum addition theorem states that the allowed values for the total angular momentum...
  50. L

    What is the significance of azimuthal quantum numbers in quantum mechanics?

    this isn't a numerical problem...thought i hope its fine posting here... i don't understand the concept of azimuthal/angular momentum quantum number.. please help. i searched this site 4 aa very basic level explanation...also the web...couldnt find much.please help!
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