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Results tagged with quantum-mechanics
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user 10001
Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.
1
vote
Why conserved quantities in quantum mechanics are experimentally interesting?
Re question 2 :
A conserved quantity is that which does not change with time. If some operator commutes with Hamiltonian operator then it will be conserved (the reason is simply because of the way tim …
- 2,087
2
votes
Expressing a unitary operator in terms of a Hermitian operator
Hermitian operators form a linear space over reals. That means if you add two given Hermitian operators (or multiply a given Hermitian operator with a real number) you again get a Hermitian operator. …
- 2,087
1
vote
Accepted
Time reversal effect on time derivative in Quantum Mechanics
Consider derivative at $t=0$; denote $\Psi(0)$ as $\Psi_{0}$
$(\partial /\partial t)T\Psi(t)\big|_{t=0}=\displaystyle lim_{h\rightarrow0}((T\Psi_{0})(h)-T\Psi_{0})/h$
Since $T\Psi$ evolves according …
- 2,087
3
votes
What is the physical meaning of commutators in quantum mechanics?
It may be helpful to assign the students following HW problem :
Suppose $A$ and $B$ be two observables
i) What is the necessary condition that $A$ and $B$ can be
simultaneously measured in …
- 2,087
3
votes
Accepted
Center of mass Hamiltonian of a Hydrogen atom
You are right; Hamiltonian for center of mass of hydrogen atom should be :
$H=\displaystyle\frac{p^2}{2(m+m_e)}$
Where $p$ is momentum of Hydrogen atom (please check what is $p$ in your book).
Now …
- 2,087
1
vote
Does the wave nature of a particle refer to the wave function?
Usual quantum mechanics is roughly based on following principles : 1. For any given ("small") physical system $S$ there is associated a set $H_S$ of physical states. 2. At any instant of time $t$ syst …
- 2,087
3
votes
magnetic moment of proton
No spin measurement of proton can give a value more or less than $\hbar/2$. But what do we mean when we say that spin of proton is $\hbar/2$ ? Spin is a 'vector' quantity (at least this is what it is …
- 2,087
9
votes
2
answers
893
views
Quantum mechanics on Cantor set?
Has quantum mechanics been studied on highly singular and/or discrete spaces? The particular space that I have in mind is (usual) Cantor set. What is the right way to formulate QM of a particle on a C …
- 2,087
4
votes
The role of representation theory in QM/QFT?
Yes, in QM/QFT we always have some group $G$ that is required to have representation on a Hilbert space. This group in particular usually includes time translation and space translation operators as i …
- 2,087
0
votes
How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?
$\psi$ can be thought of as a complex column vector with infinitely many entries indexed by the variable $x$. Entry at $x$ th position is denoted as $\psi(x)$. $|\psi(x)|^2$ is then mode square of the …
- 2,087
2
votes
State normalization in Dirac's formulation of quantum mechanics
1) Position is an observable. So,
i) For any two of its eigenstates $|q>$ and $|q'>$, we should have $<q'|q>=0$ whenever $q\neq q'$. This follows from that fact that position being an observable is i …
- 2,087
13
votes
Accepted
Proof of Canonical Commutation Relation (CCR)
As Lubos has mentioned
$QP-PQ=i\hbar$
is one of the basic requirements of quantum mechanics. Classically observables are functions of variables $q$, and $p$ and Poisson bracket relation read
$\{q, …
- 2,087