The parity operator, which is minus one to the power of the photon number operator, is a Hermitian operator and thus a quantum mechanical observable although it has no classical analogue, the concept being meaningless in the context of classical light waves. In this paper we review work on ...
The parity operator P represents the spatial inversion, SI, of the positions of all particles in an object through a fixed origin (mirror reflection involves spatial inversion) plus a rotation through π, Rπ, about an axis perpendicular to the mirror plane. ...
The term is used in two ways, first, as the operationPof spatial inversion, and the second as a numerical quantity associated with the system. Parity in the second sense is a multiplicative quantum number (► Quantum numbers) which could be + 1 or −1. In quantum mechanics the operatio...
Finite group theory plays an important role in quantum mechanics (Miller [42], Ludwig and Falter [38]). In this chapter we give an application of group theory in quantum mechanics using the parity operator. First we introduce the definition of a group and describe some of its properties. Th...
in quantum mechanics9. A Hamiltonian is called PT symmetric if it commutes with the PT operator, which requires that the real (imaginary) part of the complex potential be an even (odd) function of the coordinates. It was found later that this concept also applies to optical systems due to...
One of the fundamental axioms of quantum mechanics is associated with the Hermiticity of physical observables1. In the case of the Hamiltonian operator, this requirement not only implies real eigenenergies but also guarantees probability conservation. Interestingly, a wide class of non-Hermitian Hamilto...
The spectral renormalization method [42] and the modified squared-operator iteration method [43] can be used to obtain the numerical soliton solutions in PT-symmetric potentials. In 2014, Cole and Musslimani studied the existence and stability of gap solitons in real optical lattices with a ...
We note that the operator O^ does not affect the critical properties of the ground state since it only modifies the zero modes associated with the field f^. Since the non-Hermitian term can arise from the measurement backaction, the quantum phase transition induced by increasing gi may be ...
The concept of parity-time symmetry (PT symmetry) originates from the canonical quantum mechanics and has become a hot topic recently. As a versatile platform to investigate the intriguing concept, both theoretical and experimental works in optics have been implemented. In this paper, the PT symme...
5) symmetry transformation operator 对称变换算符 1. Five kinds of symmetry transformation operations and correspondingsymmetry transformation operators in quantum mechanics are introduced and the proof of linearity and unitary of transformation operator as well as the deduction of its formula is also given...