Application of exact solution of complex morse potential to investigate physical systems with complex and negative masses

Abstract

The interest in the study of physical systems characterized by negative and effective negative masses and their behaviour has been a subject of investigation by several researchers. The focus of the majority of these studies is experimental in nature. Inspired by the same, we have solved the Schrodinger equation for complex Morse potential with negative and complex masses and obtained its exact solution. The normalized eigenfunction and eigenvalues are obtained and the condition for admissibility of the reality of eigenvalue spectrum for the ground state of complex Morse potential has been discussed. This study establishes that it is indeed feasible for such negative masses proposed in the literature for various physical systems to be bound together by complex Morse potential. Further, we propose that atoms with complex and negative masses may bind together under the action of complex Morse-like potentials and form molecular structures.

The Effect of Negative Mass in Gravitating System<strong> </strong>

“…The broadly discussed effect of the "negative effective mass" emerges in the core-spring-shell systems exerted to harmonic excitation [1, [8][9][10]. We addressed the effect of the negative effective mass emerging in the gravitating system, which is mechanically equivalent to the core-spring-shell system.…”

“…The negative effective mass emerging in the core-spring-shell system, depicted in Figure 1A reflects the fact that the acceleration of the shell at certain conditions (to be discussed in detail below) is in the opposite direction to the applied force [1, [8][9][10]. Consequently, the chain of the core-spring-shell elements, depicted in Figure 1A demonstrates the paradoxical effective negative density [8,[11][12][13][14].…”

“…Acoustic metamaterials are defined as engineered, artificial, periodic composites enabling altering mechanic properties of materials; thus, allowing properties that are not registered naturally [16]. In particular, metamaterials with controllable and negative bulk modulus were demonstrated, exploiting the effect of the negative mass [10,[11][12][13]17]. A number of experimental exemplifications of the "negative mass effect" were already demonstrated [11][12][13][18][19].…”