# What is Quantum number: Definition and 83 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. ### What is the Largest Quantum Number for Li3+ with a 60 Å Orbital Radius?

TL;DR Summary: Quantum number of a state What is the largest quantum number of a state of the Li3+ ion with an orbital radius equal to 60 A? I tried solving the question as below
2. ### I Spin operator and spin quantum number give different values, why?

Assume spin 1/2 particle So the spin operator gives +/- hbar/2 eg. S |n+> = +/- hbar/2 |n+> But S= s(s+1) hbar = sqrt(3)/2 hbar So I'm off by a factor of sqrt(3). I suspect I am missing something fundamental about my understanding of spin. My apologies and thanks in advance.
3. ### I How azimutal quantum number got its range value

it is known that azimutal quantum number takes the values from 0 to n-1. how did they find it ?
4. ### A A good quantum number for Cnv symmetry?

Hello, I was wondering if it was possible to define good quantum numbers in solid state physics or chemistry when systems posses a discrete cylindrical symmetry Cnv. I know that in terms of angular momentum, L and L_z will be good quantum numbers for spherical symmetry, then only L_z is a good...
5. ### Finding the quantum number using Morse Potential

This problem had me take the taylor series of the Morse Potential, until I got the first non zero term. My result was U(x)=Aα2(x-x0)2. I know to find the quantum number I can use En=(n+1/2)ℏω and I know I can relate that to the potential energy of a harmonic oscillator, 1/2kx2. So if this...
6. ### I Sp3 hybridization azimuthal quantum number

The s orbital corresponds to l=0 The p orbital corresponds to l=1 For an electron in an sp3 hybridization orbital what is l?
7. ### How can I accurately calculate the quantum number of a pendulum?

Summary:: Calculate the quantum number of a pendulum I want to calculate the quantum number of pendulum. L = 1m, m = 1 kg., A= 3cm. I get a period of 2.01 sec. and f = 1/T = .498 sec. E =nhf gives me 2.67x10^31. The correct answer is 1.33x10^31, Where am I going wrong? [Thread moved from...
8. ### Principle quantum number n of the excited state

Here is a question I have been given I have started by setting up the formula and rearranging for n_2 Only problem is that I do not know the quantum number for ground state? What value do I sub in for n_1? Any help would be appreciated! Thanks
9. ### I Quantum number and group theory

Hi all, Group theory show us that irreducible representation of SO(3) have dimension 2j+1. So we expect to see state with 2j+1 degeneracy. But does group theory help to understand the principle quantum number n ? And in the case of problems with SO(3) symmetry does it explain its strange link...
10. ### Angular momentum quantum number

n is the principal quantum number. l is the angular momentum quantum number. ml is the magnetic quantum number. The possible values of l are 2, 3, and 4. I'm not sure if l can be equal to 4. On the answer key, it shows l = 2, 3.
11. ### I What does spin quantum number mean?

A spin quantum number can have a value of 1/2 or -1/2. I assume that the negative means that these two spins are in opposite directions. However, what does the 1/2 mean? Why 1/2, rather than a whole integer? Are there some sort of units associated with this value?
12. ### I Is the spin linked to the third quantum number ?

Hi everyone, As the title says, I was wondering if the third quantum number affects spin since they are both linked by magnetism. If not, will an excited particle have a different spin than a non-excited one ? Thanks for your answer and sorry for the possible mistakes, I'm just a young french...
13. ### Quantum number in hydrogen atom

Homework Statement http://i.imgur.com/GQ9Xk6d.png Homework Equations Quantum mechanical model of atomic structure The Attempt at a Solution Why all sets are allowed? H atom only got one e- which only one orbital should be there, isn't it? If there aren't second or more e- , no second...
14. ### I What is the weak isospin of hadrons?

What are the weak isospins (T3 values) of various hadrons, including the proton, neutron, mesons, hyperons and other hadrons? How is the weak isospin calculated for any hadron? Published sources provide T3 only for fundamental fermions, that is, quarks and leptons. In the fundamental bosonic...
15. ### I Quantum number and energy levels

how does the quantum number n in the wavefunction equation for a particle in a 1D box lead to increasingly well-separated energy levels? I know that the separation of energy between the levels is given by ΔE = (2n+1)h^2 / 8mL^2 which means that the higher the n, the greater the energy...
16. ### I What is the spin quantum number of an atom in 4P state?

If an atom described by spin-orbit coupling is in a 4P state, why is the spin quantum number s=3/2?
17. ### This question regarding quantum number

What is the correct set of quantum numbers for the eighth electron that fills the orbitals in an atom of oxygen? A. n = 2, l = 1, ml = –1, ms = –1/2 B. n = 2, l = 1, ml = +1, ms = –1/2 C. n = 2, l = 1, ml = +1, ms = +1/2 D. n = 2, l = 0, ml = –1, ms = +1/2 E. n = 1, l = 1, ml = +1, ms = –1/2 I...
18. ### Spin Quantum Number: Why Just Z Component?

Hello everyone, In case of hydrogen atom, when we say spin up or spin down we refer to the z component of the spin. Why are we interested only in the z component of spin and not in the x and y components? Thanks in advance
19. ### Neutral particle oscillations / quantum number conservation

Hello everyone, Why don't neutral particle oscillations have to obey conservation of (quark) flavor quantum numbers, with the example of neutral Kaon oscillations?
20. ### Understanding Valley Quantum Number in Si and Ge Band Structures

According to "Nat. Nanotechnol., vol. 7, no. 8, pp. 488–489, 2012 (http://www.nature.com/nnano/journal/v7/n8/full/nnano.2012.117.html?WT.ec_id=NNANO-201208)": Valley quantum number is associated with different crystal axes that differ only in their orientations. Such axes can support electron...
21. ### 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?
22. ### The quantum number n and its restrictions

So in class we went through the process of solving the S.W.E for the hydrogen atom. During the process a constant ##\lambda_n=\frac{ze^2}{4\pi\epsilon_0\hbar}(\frac{\mu}{2|E_n|})^{\frac{1}{2}}## is introduced, where mu represents the reduced mass of the electron. Later this constant is put on...
23. ### Probability wave peaks and quantum number

Hi, Just wanted to ask, the principal quantum number represent the number of peaks of the probability wave and I think more the value of n, more the energy of the electron as the wave has more peaks so higher frequency,am I right? Then in azimuthal quantum number, the orbitals with same energy...
24. ### Angular momentum and Quantum Number l

The question: Consider two masses of 0.1 gm each, connected by a rigid rod of length 0.5 cm, rotating about their center of mass with an angular frequency of 800 rad/s. a.) What is the value of l corresponding to this situation? b.) What is the energy difference between adjacent l-values for the...
25. ### Hydrogen Atom orbital and quantum number

I am wondering and have been thinking, exactly how does the energies of hydrogen atom orbital depend on quantum numbers? I am just curious because all of what I have learned/read discusses only one-dimensional situaiton, like a particle in a box, and I want to know how it can be applied to the...
26. ### Photon angular momentum and magnetic quantum number selection rules

For an atom, the single photon electric dipole selection rules for the magnetic quantum number require that delta_m = -1, 0 or +1. As I understand, the physical explanation for this set of selection rules is usually related to the conservation of the projection of the angular momentum on the...
27. ### Infinitely large quantum number

Hi--could someone explain how can one calculate for the root mean square fluctation in position when an electron (confined in a box) is quantum-mechanical and happens to be in a state (an infinitely large quantum number n) and why? I do know how to calculate root mean square fluctation in...
28. ### What is the INNER QUANTUM number ?

what is the INNER QUANTUM number ?
29. ### What is the lowest rotational energy level for a diatomic molecule?

My book on Physics by Beiser specifies that the rotational energy levels of a diatomic molecule are given by J(J+1)/ℏ2, where J = 0, 1, 2, 3, ... . However, in the next page, it goes on to mention that the lowest rotational energy level corresponds to J = 1. I don't see why that shouldn't...
30. ### Orbital quantum number in the shell model

Why isn't the Orbital angular momentum quantum number in the nuclear shell model restricted by the principal quantum number like it is in the atomic shell model? Also, does the principal quantum number even correspond to energy in the shell model?
31. ### Is There a Relationship Between Principal Quantum Number and Amplitude?

The principal quantum number refers to the energy of the electron in an atom, and the average distance of the electron from the nucleus. It seems to me to be analogous to the concept of amplitude for a classical wave. Is there a relation?
32. ### Magnetic quantum number and spin

Hi, please could someone provide me with an explanation of the differences between the magnetic quantum number and the spin. I thought that the magnetism of an electron/fermion comes from its intrinsic quantum angular momentum (i.e. its quantum spin) which was evidenced by the Stern–Gerlach...
33. ### Finding quantum number n of molecule

Homework Statement A nitrogen molecule (N2) has a mass of 4.68 x 10-26 kg. It is confined to a onedimensional box of length L = 100 nm. What is the approximate quantum number n of the molecule if it has a kinetic energy equal to the thermal energy kBT at room temperature? What is n if it has a...
34. ### How Does Total Spin Quantum Number Affect Symmetry in a Two-Fermion System?

I have a pair of non interacting, identical 1/2 spin fermions in a one dimensional infinite square well with walls at x=0 and x=L. One particle is in ground state, the other in first excited state. This two-particle system has total spin quantum number S=0 I have normalized energy...
35. ### Why should the quantum number m be less than equal to l.

I was reading the following article regarding solution of wavefunction of hydrogen : http://skisickness.com/2009/11/22/ To solve the angular part they gave the substitution of y = \sin \theta and then assumed that Y is a polynomial i.e. Y(y) = \sum b_n x^n and then arrived at the...
36. ### Magnetic Quantum Number Explained: Limits and Importance in Hydrogen Atom

Hi, I am going through the hydrogen atom at the moment, and I saw that the magnetic quantum number must run between ±L. I cannot find the reason in a simple enough form for me to understand, so I was hoping someone here could quickly (or slowly!) explain why ml can't be greater than L. Thanks
37. ### Principal Quantum Number of the Excited Oxygen atom.

Normally, Oxygen has 8 electrons in its neutral form that is 1s2 2s2 2p4. In this case, its principal quantum number (n) is two. But what happens if it got excited and its electronic configuration becomes 1s2 2s2 2p3 3s1? In this case, Is the principal quantum number (n) of oxygen two or...
38. ### Calculate the quantum number of an electron given its velocity

Homework Statement An electron moves with speed v=10-4c inside a one dimensional box (V=0) of length 48.5 nm. The potential is infinite elsewhere. The particle may not escape the box. What approximate quantum number does the electron have?Homework Equations En =...
39. ### Quantum mechanics problem: hypothetical spin quantum number and its

So we are doing problems involving potential energy of electrons, wave functions, and all that jazz, but I am utterly lost on how to do this problem... The professor threw it at us, and I am completely lost on how to even begin. Please help me In a different universe from ours the spin...
40. ### Atomic many-electron configurations and the use of the orbital quantum number

Hi, For single-electron atomic systems, the electron can be specified by four quantum numbers n, l, m_l, m_s (principal, orbital, z-orbital, z-spin). The orbital quantum numbers are well defined since the problem is spherically symmetric. However, for many-electron systems, the spherical...
41. ### Principal Quantum number: n to infinity?

I am aware that n is the principal quantum number and determines the energy of a specific energy level of an atom. In my notes, I see that n goes from 1,2,3... which implies to me all the way to infinity. If this is the case, why doesn't this imply that there can be infinitely many shells in an...
42. ### Does the Vibrational Quantum Number Decrease with Increasing Wavelength?

I have measured some fluorescence emission from excited iodine and am now trying to do a Birge-Sponer extrapolation. I'm just wondering if the vibrational quantum number increases or decreases with increasing wavelength? In my instructions there's a plot showing how it might look, the linear...
43. ### Rotational Quantum Number J: Understanding Its Role in Microwave Spectroscopy

Is it the same as the total angular momentum quantum number ?
44. ### Fine structure, hydrogen atom, principal quantum number 3

Homework Statement The level n=3 for atoms with 1 electron have the states 3s_{1/2}, 3p_{1/2}, 3p_{3/2}, 3d_{3/2}, 3d_{5/2}. If we ignore the spin-orbit coupling these states are degenerated. Calculate the degeneration due to the the spin-orbit coupling for the levels 3p and 3d for the...
45. ### Does the Principal Quantum Number Refer to the Electron Shell?

I was wondering, does the principal quantum number refer to the electron shell.
46. ### Question about spin magnetic quantum number

Not really a homework problem, just a question on the Pauli exclusion principle. I understand that each electron has two different spins, characterized by the possible values of the spin magnetic quantum number. However, I do not understand why it is necessary that in each orbital the two...
47. ### Why does the l quantum number depend on n?

Hi, I am a second year physicist and I have completed 2 courses on quantum mechanics. The first was a decent overview of wave mechanics and the second was only 12 lectures long and applied this knowledge to the hydrogen and helium atoms and introduced aspects of atomic and molecular physics...
48. ### Z component of spin angular momentum quantum number values

Hello, What prevents the S_z quantum number from having a value of zero? With a standard angular momentum system the quantum number can have values between -l and +l.
49. ### Total spin quantum number of helium atom with 2 electrons in first shell

Homework Statement A helium atom had two electrons in the first shell (1s). Explain, withour detailed derivation, what the value of the total spin quantum number is. Homework Equations ? The Attempt at a Solution Since the 2 electrons are in the first (1s) shell they must have...
50. ### Definition of 'good quantum number' after parity violation

Hi folks. I was always under the impression that the 'good quantum numbers' that we use to classify a particle species were always the eigenvalues of operators that commute with Hamiltonian governing that species. But it just struck me that weakly interacting particles have definite parity...