Linked Questions

4
votes
2answers
603 views

Why position and momentum operators are both continuous spectrum while angular momentum is discrete? [duplicate]

We know that position $\hat{r}$ and momentum $\hat{p}$ are both continuous spectrum operators, i.e. $$\hat{r}|r'\rangle=r'|r'\rangle, \quad \hat{p}|p'\rangle=p'|p'\rangle.$$ But the angular operator $\...
0
votes
1answer
478 views

Why do particles have spins such as $1/2$, $3/2$, $5/2$? [duplicate]

What does it mean to have 'half' spin? I have looked on Wikipedia and a few youtube videos on spin but they don't explain what it means to have $1/2$ spin. I am 18 and only starting to learning about ...
1
vote
1answer
192 views

Why must a fundamental particle's spin be a multiple of $\frac 1 2$? [duplicate]

A fermion is a particle whose spin is an odd multiple of $\frac 1 2$, and a boson is a particle whose spin is an integer. From what I've seen, these appear to be the only two possibilities; not only ...
0
votes
0answers
157 views

How does angular momentum get quantized? [duplicate]

We know that the magnitude and direction of angular momentum is quantized in quantum mechanics. We can explain the quantization with the help of quantum numbers. But actually who is responsible for ...
1
vote
1answer
50 views

Discreteness of the general angular momentum in quantum mechanics [duplicate]

When studying the general angular momentum $\textbf{J}$, which is defined as a vector operator with its components being Hermitian operators satisfying the commutation relations \begin{align*} \textbf{...
0
votes
0answers
24 views

Angular momentum of electrons in orbitals [duplicate]

Why do angular momentum of electrons in atoms are discrete value rather than being continuous ? I understand angular momentum needs to be fixed in a closed system but why I don't understand why they ...
83
votes
6answers
16k views

What is spin as it relates to subatomic particles?

I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does ...
35
votes
6answers
3k views

Reason for the discreteness arising in quantum mechanics?

What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
8
votes
3answers
2k views

Is all angular momentum quantized?

Angular momentum is definitely quantized in elementary particles and electrons in atoms. Molecules also have characteristic rotation spectra. Is it true that all angular momentum is quantized, ...
8
votes
1answer
2k views

Why is the value of spin +/- 1/2?

I understand how spin is defined in analogy with orbital angular momentum. But why must electron spin have magnetic quantum numbers $m_s=\pm \frac{1}{2}$ ? Sure, it has to have two values in ...
2
votes
2answers
2k views

Quantization of Electron Spin

Why is electron spin quantized? I've seen the derivation for the Hydrogen atom's energy levels, but my professor jumped to electrons having spin 1/2 or -1/2 as experimental. Why do electrons obey the ...
5
votes
1answer
2k views

Why is there no 1/3 spin? [duplicate]

Why do no particles have a 1/3 spin? Why are all particles' spin either a half-integer or integer? How would a particle with such a spin behave, as a fermion, boson, or neither?
1
vote
1answer
319 views

How does an isolated electron in deep space 'know' it is spinning? [duplicate]

This is a question about Mach's principle. Why is Mach's principle still an open question? In particular, if inertia arises from distant matter, Mach's principle raises the question would a particle ...
3
votes
2answers
160 views

What is the cause of discrete spectra in quantum mechanics? Both compact Lie groups and bounded Hamiltonians?

What is the mathematical cause of the "quantum" in quantum mechanics? What causes some observables to take on discrete values? There seem to be two different causes, compactness of symmetry ...
0
votes
1answer
71 views

Proof that total orbital angular momentum square can only take integer values of $\hbar^2$ [duplicate]

I am comfortable with the argument that in order for the wavefunction to be single valued/2$\pi$ invariant this means that $L_z$ must be an integer value of $\hbar$. $$U(2\pi e_z)=e^{-(2\pi i/\hbar)\...

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