Nonclassical Properties of the Hermite Polynomial Squeezed Coherent State

We introduce a new type of quantum state called the Hermite Polynomial Squeezed Coherent State (HPSCS). First, we derive the normalization factor of the HPSCS and compare its statistical properties. The Wigner function of the HPSCS is derived explicitly. The nonclassical properties of the HPSCS are explored through its photon number distribution, Mandel parameter, second-order correlation function, and the negativity of the Wigner function. The mathematical and physical properties are also studied.