QMsolve seeks to provide a solid and easy to use solver, capable of solving the Schrödinger equation for one and two particles, and creating descriptive and stunning visualizations of its solutions both in 1D, 2D, and 3D.
There are a lot of tools for making advanced quantum mechanical computations, but very few tools for visualizing them. This is the reason why we created QMsolve: To provide a tool for students for experimenting and making the subject more accessible.
In a nutshell, what it's represented in the presentation video is the probability cloud of an electron confined in a potential representing a diatomic molecule. This is the solution of the following equation (Schrödinger equation):
H ψ = E ψ
where H is the Hamiltonian, ψ is the wave function, and E is its energy.
The wavefunctions ψ that satisfy the condition from above, are called eigenstates. They represent the possible states of a particle confined in a potential whose observable energy is constant.
The eigenstates represented were computed with QMsolve with high accuracy (less than 1% of relative error) by diagonalizing 10^6 x 10^6 Hamiltonian matrix discretized using finite differences. All of this procedure is nicely encapsulated and can be easily reproduced with QMsolve minimalist object-oriented interface.
QMsolve