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Tutorials

An Introduction to Quantum Mechanics

If you are new to Quantum Mechanics read this introduction to become familiar with the main concepts and keywords. It provides the basic understanding to use SigSpace.

Ground state of wave function from a quantum well.

How to model quantum wells

Learn how to calculate the ground state of quantum wells and explore how the wave function changes across various box potentials.

Excited state with 4 nodes.

How to calculate excited states

The SigSpace solver is used to calculate the excited states of a wave function.

Example for bra-ket notation applied to Hamiltonian and for cross correlation.

How to use the bra-ket notation with SigSpace

The bra-ket notation (also known as Dirac notation) is introduced and applied to quantum states.

Example of a bloch wave over several repeated unit cells. The modulation of the repetitive wave by the k-vector creates a regular pattern.

Understand and calculate Bloch functions

Bloch's theorem is explained and applied to calculate wave functions in periodic potentials.

Example of a brillouin diagram for a repetitive box potential

Calculate Brillouin diagram for a periodic potential

The dispersion relation of a periodic potential is calculated and used to construct a Brillouin diagram.

Defines the shape of a Planar Node in an excited state.

Node Shapes in Two-Dimensions

How to determine the shape and position of nodes in two-dimensional problems.

Wave function of a hydrogen atom in 2D space.

How to calculate atomic potentials in SigSpace

How to minimize numerical errors when calculating wave functions of atoms.

Orbital shape of an ionized hydrogen molecule.

Calculate an ionized hydrogen molecule

Calculate binding length and energy of an ionized hydrogen molecule.

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