Questions tagged [wavefunction]
A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state. DO NOT USE THIS TAG for classical waves.
3,834
questions
0
votes
1
answer
80
views
How do operators on kets and wavefunctions correspond?
Let $\hat{A}$ be an operator on Hilbert space vectors. How does one show that there always exists a corresponding operator $\hat{a}$ on wave functions? i.e. $\exists \hat{a}:L^2\rightarrow L^2$ s.t. $$...
- 64.2k
3
votes
2
answers
459
views
Physical meaning of symmetric and antisymmetric wavefunction
On describing Bosons and Fermions, the symmetry of wavefunction is introduced first. Here, If two particles a and b, are in two states n and k respectively, we get the wavefunction individually. On ...
- 43
0
votes
1
answer
68
views
Non-locality of the wavefunction in QM and Twistor theory [closed]
Regarding locality, I don't think locality is a principle per se, but we often assume that the physical fields are local on spacetime, describable by partial differential equations and so on. But of ...
- 15k
2
votes
2
answers
165
views
Are there wave functions that are neither symmetric nor antisymmetric?
While proving the Pauli Exclusion Principle, one has to show that the wave function is antisymmetric for fermionic particles:
$$\Psi(x_1,x_2) = -\Psi(x_2,x_1)$$
Which is typically derived from ...
- 43
3
votes
2
answers
1k
views
On Griffith Quantum example 2.1: normalization of wave function in time.
Griffith's Quantum Mechanics example 2.1 states that:
Suppose a particle starts out in a linear combination of just two stationary states:
$$ \Psi(x,0) = c_1 \psi_1(x) + c_2\psi_2(x) $$
Find ...
- 77
0
votes
0
answers
96
views
Dirac's Bracket Notation
I have a question on Dirac's bracket notation. In particular, according to this notation, vectors and covectors are represented by $|\psi\rangle$ and $\langle\psi|$ respectively. Moreover, these two ...
- 207k
0
votes
2
answers
227
views
Boundary conditions on azimuthal component of Hydrogen atom eigenstates (Schrödinger)
I have a question relating to quantum mechanics that keeps coming back in one form or another, but it can be summed up most concisely in the context of the Hydrogen eigenstates.
When solving S.E. for ...
CommunityBot
- 1
1
vote
0
answers
24
views
Connection between dispersion relation and symmetries of the Hamiltonian
I am having trouble understanding intuitively the connection between the dispersion relation and the symmetries of the Hamiltonian. For example, suppose we have a lattice and there are four sub-...
- 324
1
vote
1
answer
88
views
Do Helium-4 atoms behave like photons?
I know that the Helium-4 atom is a boson. Does this mean that, like photons, many Helium-4 atoms can be placed at the same point in space?
How its possible? It includes fermions (Protons, Neutrons, ...
- 358k
0
votes
1
answer
47
views
Calculating the expectation value of the angular momentum operator
I'm not looking for the exact answer to the question, but rather why a certain way of solving it is chosen. We agree on the answer, but why is the approach different. I'm afraid it's a sign of me not ...
- 54.5k
1
vote
1
answer
277
views
Wave function of $s$-band with odd parity
How does a wave function of a $s$-band state with odd parity looks like (in real space)? To keep it simple, the restriction to a linear chain and a state at the $\vec{k}=0$-point might be useful.
My ...
CommunityBot
- 1
0
votes
2
answers
88
views
The eigenvectors associated to the continuous spectrum in Dirac formalism
I am comfused about the definition of an observable, eigenvectors and the spectrum in the physics litterature. All what I did understand from Dirac's monograph is that the state space is a complex ...
- 126k
0
votes
2
answers
64
views
Quantum Mechanical Current Normalisation
Consider an electron leaving a metal. The quantum-mechanical current operator, is given (Landau and Lifshitz, 1974) by
$$
j_x\left[\psi_{\mathrm{f}}\right]=\frac{\hbar i}{2 m}\left(\psi_{\mathrm{f}} \...
- 25.3k
2
votes
1
answer
106
views
Derivation of Schrödinger equation in Feynman-Hibbs
I am going through the derivation in chapter 4-1 of "Quantum Mechanics and Path Integrals. Emended Edition" by Feynman and Hibbs. The chapter starts with a proof of the equivalence of the ...
- 207k
2
votes
1
answer
45
views
Phase Coherence in the BCS wavefunction and the Cooper Pair Wavefunction
I have a couple question regarding the following BCS wavefunction ($|0\rangle$ is the vacuum state):
$$|\psi\rangle = \Pi_k \big(|u_k|+|v_k|e^{i\varphi}c^\dagger_{k\uparrow} c_{-k\downarrow}\big)|0\...
- 91