Quantum tunneling from family of Cantor potentials in fractional quantum mechanics

Singh, Vibhav Narayan; Umar, Mohammad; Hasan, Mohammad M.; Mandal, Bhabani Prasad

doi:10.1016/j.aop.2023.169236

Cited by 3 publications

(1 citation statement)

References 49 publications

(77 reference statements)

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“…Driven by its theoretical significance and potential practical applications, extensive investigations have explored how matter waves propagate through various potential distributions [7,8]. Such efforts span a diverse array of quantum mechanical domains, including non-Hermitian quantum mechanics (NHQM) [9][10][11][12], space-fractional quantum mechanics (SFQM) [13][14][15][16][17][18], and quaternionic quantum mechanics (QQM) [19][20][21][22][23][24][25]. With an array of contributions over the past century, quantum tunneling and the associated analytical calculations of scattering coefficients continue to be a focal point of quantum research [1][2][3][4][5][6][7][8][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Tunneling from general Smith–Volterra–Cantor potential

Singh

Umar

Hasan

et al. 2023

Journal of Mathematical Physics

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We study the tunneling problem from the general Smith–Volterra–Cantor (SVC) potential of finite length L characterized by the scaling parameter ρ and stage G. We show that the SVC( ρ) potential of stage G is a special case of the super periodic potential (SPP) of order G. By using the SPP formalism developed by us earlier, we provide the closed form expression of the tunneling probability T G( k) with the help of the q-Pochhammer symbol. The profile of T G( k) with wave vector k is found to saturate with increasing stage G. Very sharp transmission resonances are found to occur in this system, which may find applications in the design of sharp transmission filters.

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