All Questions
7 questions
1
vote
1
answer
142
views
Can a wave function discontinuous in the time variable be a solution of the Schrödinger equation?
It is well known that wave functions that are discontinuous in the space variable cannot be solutions of the Schrödinger equation, because the Schrödinger equation is a second-order differential ...
- 29
2
votes
1
answer
191
views
Decay of the First Derivative of the Quantum Wave Function
I understand that the Hilbert space of all physical solutions of the Schrodinger equation have the property where
$$
\lim_{x\to\infty}\Psi=0
$$
For one of my assignments, I wanted to use
$$
\lim_{x\to\...
- 65
1
vote
1
answer
54
views
Proof of differentiate form of dynamical semigroups
I am studying some basics of the pure mathematical background for open quantum systems from Angel Rivas`s book which is "Open quantum systems, an introduction".
Here is a theorem (Page 6, ...
- 119
2
votes
2
answers
465
views
Variation of a time-ordered exponential
Consider the time-ordered exponential (Wilson line):
$$
U(t_{f},t_{i})
=
\mathcal{T}\text{exp}\left(-i\int_{t_{i}}^{t_{f}}\mathcal{A}(t)dt\right)\tag{1}
$$
Where $\mathcal{A}(t)$ is some matrix-valued ...
- 587
5
votes
1
answer
909
views
General derivative of the exponential operator w.r.t. a parameter
I am interested in the calculation of the general $N$th derivative w.r.t. a parameter $\lambda$ of a quantum mechanical exponential operator with the following structure:
\begin{equation*}
\frac{\...
- 385
3
votes
1
answer
2k
views
How does one properly define the derivative of one operator-valued function?
In Quantum Mechanics we usually consider operator-valued functions: these are functions that take in real numbers and gives back operators on the Hilbert space of the quantum system.
There are ...
- 37.4k
12
votes
1
answer
1k
views
Time derivative of the state vector as expressed in abstract Hilbert space vs. as a wavefunction
The Schrodinger equation in Hilbert space is expressed as : $$\frac{\partial}{\partial t} \psi(t) = \frac{-i}{\hbar}H\psi(t). $$
Here $\frac{\partial}{\partial t} \psi(t) \equiv \psi'(t) \equiv\lim \...
- 421