Schwartz distributions that have all the properties of coherent states

What is it about?

Due to their remarkable properties, coherent states are sometimes more convenient to use than an orthonormal basis in a Hilbert space. In this paper, we show that a family of Schwartz distributions can have all the key properties of coherent states. Therefore, it can be successfully used instead of the family of ordinary coherent states and called coherent Schwartz distributions.

Featured Image

Photo by Raül Santín on Unsplash

Photo by Raül Santín on Unsplash

Why is it important?

For operators with a continuous spectrum, coherent Schwartz distributions are more natural than normalized coherent states. In addition, they have a simpler design. The coherent distributions can be used as integral kernels of coherent transforms. They can also be used to construct operator-irreducible representations for algebras that have Casimir elements with a continuous spectrum.