# Questions tagged [schroedinger-equation]

Partial differential equation which describes the time evolution of the wavefunction of a quantum system. It is one of the first and most fundamental equations of quantum mechanics.

2,163 questions
Filter by
Sorted by
Tagged with
0answers
22 views

### Infinite 3D sphere well with Dirac Delta potential function at the origin

A spinless particle of mass $m$ is constrained in a 3D region of zero potential within an impenetrable spherical shell of inner radius $r = a$, with a delta function potential at the origin given that ...
0answers
24 views

### How does the wave function relate to probability?

I'm trying to solve this problem which involves the probability of a particle being in a certain region. I know that $|\Psi|^2$ is the probability density, but how do I get this in the region?
0answers
57 views

1answer
44 views

0answers
15 views

### Why do we sometimes transfrom the interaction picture back into the Schrodinger picture?

We go first into the interaction picture, then say do a rotating wave approximation and then go into the rotating frame of the driving frequency, we solve the schrodinger equation and then and the end ...
3answers
81 views

### Can the initial wavefunction be discontinuous?

In a infinite potential well of width $a$, an electron starts in the left half and at $t=0$; it is equally likely to be found at any point in that region. To find the wavefunction at later times, we ...
2answers
216 views

### Coefficients of the wave function - a free particle in a box [closed]

If we solve the time independent Schrödinger equation for a particle in a box of length $L$, we get: $$\psi_n\left(x\right)=A\sin\left(\frac{\pi n}{L}x\right)$$ I then see that we normalize $A$ such ...
2answers
145 views

### Critique on various ways to think about time reversal transformation on Schrodinger equation?

Please define how time-reversal symmetry act on Schrodinger equation $i \frac{\partial}{\partial t} |\Psi{}(t) \rangle = H(t) |\Psi{}(t) \rangle.$ (for general form: which can be relativistic such as ...
1answer
93 views

### What is the difference between the time dependent and time independent Schrödinger equation?

I've already gone through a couple of questions regarding the Schrödinger equation and none of them seem to solve my doubt. Some say that the Time Independent Schrödinger Equation (TISE) is just a ...
1answer
47 views

### Is the linear combination of eigenfunctions of a time-independent Hamiltonian also a solution of the time independent Schrodinger equation?

Consider a system where the Hamiltonian is time independent, the wavefunction which is say a linear combination of the eigenfunction of the Hamiltonian (with different eigenvalues) is not the solution ...
1answer
31 views

### Number of states in the free electron gas

Considering the free electron gas model and the representation of stationary states in the k-space, the book I'm reading (Griffith's Introduction to Quantum Mechanics) says that "each ...
1answer
53 views

2answers
388 views

### Adding a constant term to potential in Schrödinger's Equation

If we add a constant term $k$ to the potential function in time-independent Schrödinger's equation, $V(x) \rightarrow V(x)+k$, then how does it affect the solution, and what is its significance? ...
0answers
20 views

### Similarity in the solution for diffusion and Schrödinger equations [duplicate]

Both diffusion and Schrödinger equations are PDEs (first order in time and second order in space) with a different physical meaning. When solving a simple case of 1d diffusion with fixed boundary ...
2answers
118 views

### Why is the phase of a matter wave not Galilean invariant? And what does this say about the Schrödinger equation? [duplicate]

Matter waves are not Galilean Invariant Consider a non-relativistic freely-propagating matter wave in an inertial frame $\Sigma'$ moving along the $x'$-direction with kinetic energy $E'=1/2m_0v'^2$, ...