Non-local energy density functional for atoms and metal clusters

Ordering Ambiguity Revisited via Position Dependent Mass Pseudo-Momentum Operators

“…They are used in the energy density many-body problem [1], in the determination of the electronic properties of the semiconductors [2] and quantum dots [3], in quantum liquids [4], in 3 He clusters [5] and metal clusters [6], in the Bohmian approach to quantum theory (cf., e.g. [7]), in the full and partial wave-packet revivals(cf., e.g., [8]), etc.…”

The quantum effective mass Hamilton–Jacobi problem

“…Let ξ 1 , ξ 2 and χ 1 , χ 2 satisfy (20) and (19) on a neighborhood S. If ξ 1 and ξ 2 are linearly independent, then; , then x 0 is a simple pole of f . By using (19), f becomes analytic at x 0 . And there is a contradiction.…”

“…On the other hand, position dependent mass model has been a subject of considerable interest in recent years [13][14][15][16][17][18][19][20][21][22] following the work of Von Roos and Levy-Leblond [17,20] that claims to describe some physical phenomena.…”

d-dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

“…It constitutes an interesting and useful model for the study of many physical problems. In the energy density functional settings to the many-body problem [1], the non-local term of the associated potential can be often expressed as a position-dependence of an appropriate effective mass M (r). Such an effective mass concept is used, for example, in the determination of the electronic properties of the semiconductors [2] and quantum dots [3], in quantum liquids [4], in 3 He clusters [5] and metal clusters [6].…”

“…A position-dependent effective mass associated with a quantum mechanical particle in the Shrödinger equation have attracted intense research activities over the years [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. It constitutes an interesting and useful model for the study of many physical problems.…”