# What is In quantum mechanics: Definition and 256 Discussions

In quantum physics, a measurement is the testing or manipulation of a physical system in order to yield a numerical result. The predictions that quantum physics makes are in general probabilistic. The mathematical tools for making predictions about what measurement outcomes may occur were developed during the 20th century and make use of linear algebra and functional analysis.
Quantum physics has proven to be an empirical success and to have wide-ranging applicability. However, on a more philosophical level, debates continue about the meaning of the measurement concept.

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1. ### Allowed energy for a potential in quantum mechanics

Hi, I'm working on a problem where I need to find the different energies allowed for a potential, and I found this link https://quantummechanics.ucsd.edu/ph130a/130_notes/node151.html, which is similar of what I'm doing. I'm using mathematica to find the values of E. However, I'm not sure how...
2. ### I "No objective reality" in quantum mechanics?

As per title and the TL;DR, I'm curious if there could be some truth in these statements of the headlines I had read recently or are they just sensationalist fluff. Personally, I find these statements very hard to believe. In fact, impossible to believe. But I'm not a QM expert, not even an...
3. ### A Power series in quantum mechanics

Just earlier today i was practicing solving some ODEs with the power series method and when i did it to the infinite square well i noticed that my final answer for ##\psi(x)## wouldn't give me the quantised energies. My solution was $$\psi(x) = \sum^{\infty}_{n=0} k^{2n}(\cos(x) + \sin(x))$$...
4. ### B Statistical Independence in Quantum Mechanics

Very basic question here, about statistical independence in quantum mechanical experiments. The quote from PD below is what prompted the question. When we talk about "some kind of pre-existing correlation" are talking about a simple correlation in the sense of the correlation of sunglasses and...
5. ### A Position basis in Quantum Mechanics

Can I conceive a countable position basis in Quantum Mechanics? How can I talk about the position basis in the separable Hilbert space?
6. ### I Particle on a sphere problem in quantum mechanics and its solution

To solve a particle on a sphere problem in quantum mechanics we get the below equation :##\left[\frac{1}{\sin \theta} \frac{d}{d \theta}\left(\sin \theta \frac{d}{d \theta}\right)-\frac{m^{2}}{\sin ^{2} \theta}\right] \Theta(\theta)=-A \Theta(\theta) ## To solve this differential equation, we...
7. ### I Inner products with spherical harmonics in quantum mechanics

Let ##|l,m\rangle## be a simultaneous eigenstate of operators ##L^2## and ##L_z## and we want to calculate ##\langle l,m|cos(\theta)|l,m'\rangle## where ##\theta## is the angle ##[0,\pi]##. It is true that in general ##\langle l,m|cos(\theta)|l,m'\rangle=0## ##(1)## for the same ##l## even if...
8. ### I Definition of magnetic moment in quantum mechanics

* The general formula for the magnetic moment of a charge configuration is defined as ##\vec{\mu} = \frac{1}{2} \int \vec{r} \times \vec{J} \,d^3r##* For an electron it's said that the correct equation relating it's spin and magnetic moment is is ##\vec{\mu} =g\frac{q}{2m}\vec{S}## * It's...
9. ### I A thought experiment concerning determinism in quantum mechanics

According to the uncertainty principle, when we measure a micro-object with a measuring device, we cannot predict what value the device will show. But if we knew exactly the wave function of this device, together with the wave function of the micro-object, could we exactly predict the result of...
10. ### Phase factor in quantum mechanics

Please be kind to help.I would be grateful

48. ### Question about phase factor in Quantum Mechanics

Homework Statement I am trying to understand a solution to a problem. I may not need to post the entire question, I just need to know if ##-i = e^{\frac{-i*pi}{2}}## Homework EquationsThe Attempt at a Solution the reason for this question is that one step of the problem has a quantity...
49. D

### Constants of motion in quantum mechanics

Homework Statement A particle of mass m and spin s, it's subject at next central potential: ## \begin{equation*} V(\mathbf{r})= \begin{cases} 0\text{ r<a}\\ V_0\text{ a<r<b}\\ 0\text{ r>b} \end{cases} \end{equation*} ## Find the constants of motion of the system and the set of...
50. ### A Rigged Hilbert Spaces In Quantum Mechanics

In discussing stuff in another thread I used the standard Dirac notion expanding a state in position eigenvectors namely |u> = ∫f(x) |x>. By definition f(x) is the wave-function. I omitted the dx which is my bad but the following question was posed which I think deserved a complete answer. It...