Incoming links: Complex number
Group of the unitary matrices.
Complex analogue of the orthogonal group.
One notable difference from the orthogonal group however is that the unitary group is connected "because" its determinant is not fixed to two disconnected values 1/-1, but rather goes around in a continuous unit circle. is the unit circle.
Complex analogue of orthogonal matrix.
Applications:
- in quantum computers programming basically comes down to creating one big unitary matrix as explained at: quantum computing is just matrix multiplication
Why are complex numbers used in the Schrodinger equation? Updated 2024-12-15 +Created 1970-01-01
Why is there a complex number in the equation? Intuitively and mathematically:
Necessity of complex numbers in the Schrödinger equation by Barton Zwiebach (2017)
Source. This useless video doesn't really explain anything, he just says "it's needed because the equation has an in it".
The real explanation is: they are not needed, they just allow us to write the equation in a shorter form, which is always a win: physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600