**Bohr-Sommerfeld quantization rule in noncommutative space**

**Abstract:**

There is no possibility to measure coordinates more accurate than some minimal length in the string theory [1].
To reproduce this property of
the string theory Kempf proposed to modify commutation relation between the coordinate and the momentum operator in the
following way [2]:
*[X,P]=if(P)*.
Value of the minimal length can be determined from this relation.

We developed the WKB approximation for the case of the above modification and on its basis we derived the
Bohr-Sommerfeld quantization rule [3]. We also
generalized the Bohr-Sommerfeld quantization rule for the case
*[X,P]=if(X,P)*.
Such a modification is characterized by minimal momentum uncertainty as well as the minimal length.

We compared the spectra obtained with the help of the Bohr-Sommerfeld quantization rule with exact ones for several examples.

[1] D.J. Gross and P.F. Mende, Nucl. Phys. B303,
407 (1988).

[2] A. Kempf, G. Mangano and R.B. Mann, Phys. Rev. D52, 1108 (1995).

[3] T.V. Fityo, I.O. Vakarchuk and V.M. Tkachuk, J. Phys. A39, 379 (2006).

Joint work with I.O. Vakarchuk and V.M. Tkachuk.