# What is Singlet: Definition and 63 Discussions

In quantum mechanics, a singlet state usually refers to a system in which all electrons are paired. The term 'singlet' originally meant a linked set of particles whose net angular momentum is zero, that is, whose overall spin quantum number

s
=
0

{\displaystyle s=0}
. As a result, there is only one spectral line of a singlet state. In contrast, a doublet state contains one unpaired electron and shows splitting of spectral lines into a doublet; and a triplet state has two unpaired electrons and shows threefold splitting of spectral lines.

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1. ### I Singlet Halperin State Construction

Hi all, I'm reading through David Tong's Fractional Quantum Hall Effect notes right now and am stumped by how he constructs the singlet Halperin state (the last equation in this document: https://www.damtp.cam.ac.uk/user/tong/qhe/three.pdf, on page 116 as per the document page number at the...
2. ### A Mixed versus Pure Quantum States for the Singlet

I have some basic questions about mixed states and entanglement. 1. Do mixed states always imply that the states are entangled and vice versa? 2. Can mixed states ever be separable? 3. Does interference have anything to do with entanglement? In terms of Density Matrices, ρ = |ψ><ψ|: 4...
3. ### A Why do Eu doped phosphors show fluorescence property without singlet?

As it is mentioned fluorescence is a singlet to singlet transition and this is the reason that fluorescence is a fast process. now consider the Eu doped phosphor material where 5D0--->7F2 and other transitions show the prominent intensity peaks in down-conversion process. those are not singlet...

5. ### I Are Hadrons and Gluons Symmetric Against Interchange of Colours?

This is from Griffiths' Elementary Particles, section 8.4.1. By analysing the colour factor, the conclusion is that a quark/anti-quark pair attract in the colour singlet configuration: $$\frac 1 {\sqrt 3}(r\bar r + b \bar b + g \bar g)$$ And this explains (to some extent) why mesons are...
6. ### Invariance of a spin singlet under rotation

I have tried doing the obvious thing and multiplied the vectors and matrices, but I don't see a way to rearrange my result to resemble the initial state again: ##(\mathcal{D_{1y}(\alpha)} \otimes \mathcal{D_{2y}(\alpha)} )|\text{singlet}\rangle = \frac{1}{\sqrt{2}}\left[ \begin{pmatrix}...
7. ### Energy of singlet state and triplet state

The picture shown below is one triplet state and one singlet excited state of molecular orbitals. According to Hund's Law, the triplet state, which has 2 electrons with parallel spin, has lower energy than the singlet state. I went through some papers, only to be told that the triplet state has...
8. ### Why are most molecules in the singlet state instead of the triplet state?

Most molecules are in singlet ground state which is of higher energy than triplet lower energy state .According to thermodynamics molecule tend to remain in lower energy state.Therefore,I presume molecules should remain in triplet state .Could anyone clarify my point
9. ### I Invariant symbol implies existence of singlet representation

I don't understand what the last paragraph of the attached page means. Why does the Kronecker delta being an invariant symbol mean that the product of a representation R and its complex conjugate representation has the singlet representation with all matrices being zero? Doesn't the number...
10. ### I How can electrons have the same spin in triplet state?

Hello, I don't understand how can electrons in triplet state can have the same value of spin? Shouldn't the spins be different because two fermions can't have the same state? The following picture explain my question in more detail.
11. ### I LS-Coupling: intuition why 2p^2 has no singlet P?

I get the microstate-counting approach to finding the term symbols for a given configuration. But based on what I know about addition of angular momentum in quantum mechanics, I feel like there's a conceptual gap. When I do the microstate counting on the 2p##^{2}## configuration, I get singlet...

18. ### I Singlet and triplet spin states - the normalisation constant

The triplet spin state with a normalisation constant of 1/√2 and the singlet spin state with the same normalisation constant... Where on Earth is this normalisation constant derived from? I've been scouring the Griffiths intro to quantum mechanics textbook and can't find info on it.
19. ### Relation b/w probability of triplet state and singlet state

Homework Statement [/B] If electron (1) is in a state described by cosα1χ+ + sinα1e iβ1 χ- and electron (2) is in a state described by cosα2χ+ + sinα2e iβ2 χ-, what is the probability that the two-electron state is in a triplet state? The Attempt at a Solution I already solved this problem; I...
20. ### Total spin of triplet and singlet states

I'm a litte confused about spin triplet and singlet states. How do we know that for ↑↓+↓↑ the total spin S is 1, and for ↑↓-↓↑ the total spin S is 0? Also, how is total ms computed for these two states? (I understand that they are both 0, but not sure where that comes from) Thank you very much...
21. ### Physical difference between singlet and triplet states

Hey! How are the two m=0 spin states (<up,down> + <down,up>) and (<up,down> - <down,up>) physically different? I realize that according to the math, the first one has a total spin of ##2 \hbar## while the second has a total spin of ##0##. But wouldn't you, intuitively, expect both states to...
22. ### Wavefunctions of Singlet and Triplet States

If we have a system of two electrons, addition of angular momentum tells us that the spin states of the composite system can be decomposed into those of the two electrons as follows |1,1>=|+>|+> |1,0>=(|+>|-> + |->|+>)√2 |1,-1>=|->|-> |0,0>=(|+>|-> - |->|+>)√2 where the states are |s,ms> for the...
23. ### What is the Slater determinant of a singlet or a triplet?

We have a system of 2 particles, let's say with following hamiltonian: $$\hat{H} = -\frac{\hbar^2\hat{\nabla}_1^2}{2m} -\frac{\hbar^2\hat{\nabla}_2^2}{2m}$$ The eigenstates are often represented as (spatial wavefunction)*(spin wavefunction), where the spin wavefunction is a singlet or a...
24. ### How do you get the color singlet combination of quarks?

I was reading my book and it states that the lack of anti-symmetry in the total wave function of the Δ++ particle led to the introduction of the missing degree of freedom, or color. It states that free particles are colorless so they must be in color singlet states. From there, it just lists the...
25. ### How Does Particle Proximity Affect Transition Probability to the Singlet State?

QM students study the singlet state, (|u>-|d>)/SQRT(2). Particles in the singlet state can be separated by any distance, and remain in the singlet state. That leads to the EPR paradox, Bell's Theorem and the more. My question has more to do with entering the singlet state. Leonard Susskind...
26. ### Triplet and Singlet Helium States

I have a theoretical question, I just recently learned that the spin triplet S=1 of helium in the state 1s2s is lower in energy than the 1s2 state due to the exchange interaction. I then learned that this 1s2s state has a shorter lifetime than the 1s2 state, can anyone explain why this occurs...
27. ### Singlet and Triplet Terms misunderstanding

I am a little unclear on why in atomic physics that the total orbital momentum terms have to be specifically singlet or triplet states, for example G -Singlet F -Triplet D -Singlet P -Triplet S -Singlet I think it has to do with the pauli exclusion principle but don't really understand the...
28. ### Can Singlet Spin Pairs Behave Like Bosons?

I just studied about the QM of singlet spin pairs. I have additional questions. Neither Wikipedia, nor past threads on this forum seem to address the questions. 1) A pair of electrons forming a singlet pair A. Can the pair be split again into non-entangled electrons? If yes how; just hit...
29. ### Question on angular momentum of triplet and singlet wavefunctions

Hi, I'm relatively new to QM so just a basic explanation of my problem would be amazing! I'm doing some internet research on superfluidity over my summer holiday, and was looking specifically at 3He, and the way it forms Cooper pairs. Having read a classical analogy to why the relative angular...
30. ### Expectation value of composite observable in singlet state

Homework Statement I've been reading Leonard Susskind's Theoretical Minimum volume on QM, and enjoying it quite a bit - the book doesn't include exercise solutions at the end though, and if they exist online for this volume I haven't been able to find them. (Perhaps if such solutions...
31. ### How can I construct singlet, triplet, and more with S=1 ions?

I've learned how to construct singlet and triplet with two S=1/2 particles, i.e., electrons. How can I generalize it to system with two S=1 ions? Furthermore, I wonder what is the general principle to make a quantum entity with n-particle S=m systems. Thank you in advance.
32. ### Ground state: singlet or triplet

In my book it is mentioned that for the two 1s electrons the ground state is the singlet while for the two 2p electrons the ground state could be either singlet or triplet. Generally how can you determine whether the ground state is singlet or triplet?
33. ### Eta prime meson as SU(3) singlet

I understand that when the quark theory was being developed that SU(3) was used to explain the mesons that were ultimately found to be composed of the up, down, and strange quarks. I also get that the SU(3) is grouped as an octet and a singlet, with the eta prime meson being the singlet. But I'm...
34. ### Singlet and triplet states of H2

Homework Statement The wave function for a system of two hydrogen atoms can be described approximately in terms of hydrogen wave functions. (a) Give the complete wave functions for the lowest states of the system for singlet and triplet spin configurations. Sketch the spatial part of each...
35. ### Differences between the triplet and singlet states

What are the differences between the triplet and singlet states. triplet state-- parallel spins-- S=1 , 2S+1=3 Singlet state-- Paired spins---S=0 , 2S=1= 1 singlet state has paired spins of electrons in the same orbit, thus there are repulsion force between the two electron in the same...
36. ### How does singlet oxygen work in pericyclics?

and here's the diagram for the 1O2 dienophile: Its the 1E+g the one I'm interested in. I see that its single electrons are in a couple of degenerate pi orbitals. I'm having trouble figuring out what the LUMO is here. Does it even matter that I have 2 LUMOs? I kinda suspect, that would make it...
37. ### Singlet oxygen in combustion-(Why is it not being used)?

Over the last few days I have been studing combusiton reactions. I have found numerous papers that all state singlet oxygen can increase the combustion efficiency. My question is: Why is singlet oxygen not being used in todays automibiles? It seems to me the only issue would be...
38. ### Spin expectation value of singlet state from two axes

Homework Statement Homework Equations The Attempt at a Solution I am just trying to figure out how to start the problem. Any help would be greatly appreciated.
39. ### How can we demonstrate hadrons in QCD must be color singlet?

Coupling constant of strong interaction is only finitely greater than coupling constant in QED if the quarks insides hadron not very far apart each other,so I do not understand why there are not exist color multiplet states of hadrons,other hand I do not understand why the singlet states have...
40. ### Status of the Complex Singlet Extensions?

It has be mentioned the real singlet extension of the Standard Model by Chamseddine and Connes. But I favour a pair of charged scalars, so, question: what is the status of the Complex Singlet Extensions of the Standard Model, or their susy versions? Are they still there?
41. ### Two-electron Ground State of a Spin-Independent Hamiltonian is a singlet

Homework Statement The problem is from Ashcroft&Mermin, Ch32, #2(a). (This is for self-study, not coursework.) The mean energy of a two-electron system with Hamiltonian \mathcal{H} = -\frac{\hbar^2}{2m}(∇_1^2 + ∇_2^2) + V(r_1, r_2) in the state ψ can be written (after an integration by...
42. ### If the singlet gluon existed (and I realize it doesn't)

OK, here's a question that's unusual in that it regards a particle state that's pretty much taken to be nonexistent. Nonetheless, my curiosity is piqued. I've read from multiple sources that if the singlet gluon existed, it would couple with equal strength to all baryons because they are also...
43. ### Bell tests: Singlet vs Triplet State

This topic came up in another discussion and I said I’d start a new thread for it. I had speculated that to experimentally demonstrate Bell violations, you needed particles in the spin singlet state; in particular, photons in the spin triplet state would not be especially distinguishable from...
44. ### Why is a deuteron an antisymmetric singlet in

Why is a deuteron an antisymmetric singlet in isospin: |\uparrow\downarrow>-|\downarrow\uparrow>=|0,0> whereas a proton and neutron that are separated are a combination of an antisymmetric singlet and a symmetric triplet: |\uparrow\downarrow>=|0,0>+|1,0> I don't understand the difference...
45. ### What is a singlet under SU(3)?

what is a singlet under SU(3)?
46. ### Local deterministic model of singlet state correlations

Phys. Rev. Lett. 105, 250404 (2010) Local deterministic model of singlet state correlations. The derivation of Bell inequalities requires an assumption of measurement independence, related to the amount of free will experimenters have in choosing measurement settings. Violation of these...
47. ### How Does the Exclusion Principle Affect Energy Levels in Electron Spin States?

Hi guys! When we consider a system composed by two 1/2 spin particle we can label the 4 natural basis vector by the individual spin of each particle, i.e. |++>,|+->,... , or by the eigenvalues of the total spin S and its projection M. In the latter case we have again 4 basis vectors: a singlet...
48. ### What is meant by singlet and triplet state of an electron system?

What is meant by singlet and triplet state of an electron system? Thanks in Well advance...
49. ### How do we calculate spin functions and determine singlet and triplet states?

Hi there, I would be most grateful if someone would explain how do we calculate the spin function χ(s_1,s_2 )=1/√2 [α(s_1 )β(s_2 )±α(s_2 )β(s_1 )] both the symmetric and antisymmetric α(s_1 )β(s_2 )+α(s_2 )β(s_1 ) = ? α(s_1 )β(s_2 )-α(s_2 )β(s_1 ) = ? knowing that α( + 1 / 2) = β(...
50. ### Entanglement correlations, singlet spin state

Let's say you have a pair of electrons in the singlet spin state. I thought that Alice measuring the spin of one electron (about the "z axis") corresponded to applying the operator \hat{S}_z\otimes \hat{I} (where \hat{I} is the identity operator) to the singlet state \frac{1}{\sqrt{2}}(\uparrow...