Tagged Questions
3
votes
1answer
133 views
How does a state in quantum mechanics evolve?
I have a question about the time evolution of a state in quantum mechanics. The time-dependent Schrodinger equation is given as
$$
i\hbar\frac{d}{dt}|\psi(t)\rangle = H|\psi(t)\rangle
$$
I am ...
2
votes
2answers
424 views
Two expressions for expectation value of energy
I was looking up expectation value of energy for a free particle on the following webpage:
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/expect.html
It says that $E=\frac{p^2}{2m}$ and ...
2
votes
1answer
308 views
Solving time dependent Schrodinger equation in matrix form
If we have a Hilbert space of $\mathbb{C}^3$ so that a wave function is a 3-component column vector
$$\psi_t=(\psi_1(t),\psi_2(t),\psi_3(t))$$
With Hamiltonian $H$ given by
$$H=\hbar\omega
...
1
vote
1answer
83 views
Where can I find hamiltonians + lagrangians?
Where would you say I can start learning about Hamiltonians, Lagrangians ... Jacobians? and the like?
I was trying to read Ibach and Luth - Solid State Physics, and suddenly
(suddenly a Hamiltonian ...
1
vote
1answer
274 views
The Hermiticity of the Laplacian (and other operators)
Is the Laplacian operator, $\nabla^{2}$, a Hermitian operator?
Alternatively: is the matrix representation of the Laplacian Hermitian?
i.e.
$$\langle \nabla^{2} x | y \rangle = \langle x | ...
5
votes
3answers
464 views
What is the relationship between Schrödinger equation and Boltzmann equation?
The Schrödinger equation in its variants for many particle systems gives the full time evolution of the system. Likewise, the Boltzmann equation is often the starting point in classical gas dynamics.
...
