Particle in a quantum well with a moving wall

Torabi, Reza; Rezaei, Zahra

doi:10.18869/acadpub.ijpr.17.1.133

Particle in a quantum well with a moving wall

Authors

Reza Torabi

Zahra Rezaei

https://doi.org/10.18869/acadpub.ijpr.17.1.133

Abstract

We study the problem of a quantum particle in an infinite one dimensional potential well with a moving wall. Based on the effective Hamiltonian approach and using the gauge transformation concepts, we show that the effect of the moving wall appears as an extra phase factor in the wave function which depends on the velocity of the wall.

Keywords

Time dependent boundary conditions

Infinite quantum well

Gauge transformation

Dirac phase

[1] S. W. Doescher and M. H. Rice, Am. J. Phys. 37 (1969) 1246.
[2] D. N. Pinder, Am. J. Phys. 58 (1990) 54.
[3] S. T. Dembinski, A. J. Makowski, and P. Peplowski, J. Phys. A: Math. Gen. 28 (1995) 1449.
[4] M. G. E. da Luz and B. K. Cheng, J. Phys. A: Math. Gen. 25 (1992) 2033.
[5] P. Seba, Phys. Rev. A 41 (1990) 2306.
[6] C. Scheiniger and M. Kleber. Physica D 50 (1991) 391.
[7] A. J. Makowski and S. T. Dembinski, Phys. Lett. A 154 (1991) 217.
[8] A. J. Makowski and P. Peplowski, Phys. Lett. A 163 (1992) 142.
[9] A. J. Makowski, J. Phys. A: Math. Gen. 25 (1992) 3419.
[10] P. Pereshogin and P. Pronin, Phys. Lett. A 156 (1991) 12.
[11] A. Munier, J. R. Burgan, M. Feix, and E. Fijalkow, J. Math. Phys. 22 (1981) 1219.
[12] M. V. Berry and G. Klein, J. Phys. A: Math. Gen. 17 (1984) 1805.
[13] D. M. Greenberger, Physica B 151 (1988) 374.
[14] A. Devoto and B. Pomorisac, J. Phys. A: Math. Gen. 25 (1992) 241.
[15] A. Mostafazadeh, J. Phys. A 32 (1999) 8325.
[16] V. V. Dodonov, A. B. Klimov, and D. E. Nikonov, J. Math. Phys. 34 (1993) 3391.
[17] A. Shapere and F. Wilczek, Geometric Phases in Physics, World Scientific (1989).
[18] M. Mehrafarin and R. Torabi, Phys. Lett. A 373 (2009) 2114.
[19] R. Torabi and M. Mehrafarin, JETP Lett. 95 (2012) 277.
[20] P. J. Leek, J. M. Fink, A. Blais, R. Bianchetti, M. Göppl, J. M. Gambetta, D. I. Schuster, L. Frunzio, R. J. Schoelkopf, and A. Wallraff, Science 318 (2007) 1889.
[21] A. A. Abdumalikov, J. M. Fink, K. Juliusson, M. Pechal, S. Berger, A. Wallraff, and S. Filipp, Nature 496 (2013) 482.
[22] P. A. M. Dirac, Proc. Roy. Soc. A 133 (1931) 60.
[23] K. Yu. Bliokh and Yu. P. Bliokh, Ann. Phys. 319 (2005) 13.
[24] R. Torabi and Z. Rezaei, Phys. Lett. A 337 (2013) 1668.
[25] R. Torabi, Physica B 407 (2012) 2109.
[26] A. Messiah. “Quantum mechanics”, Vol. 2, North-Holland, Amsterdam (1966).