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$$ (20) A series of transformations results in the following expressions for the wave function and energy spectrum of CC: $$\varphi (x) = ch^\lambda \left( \fracx\gamma \right)\left[ {C_1 \cdot {}_2F_1 \left( u,v,\frac12;1 - ch^2 \left( \fracx\gamma \right) \right) } \right. \left. {+ C_2 \left( 1 - ch^2 \left( \fracx\gamma \right) \right)^\frac12 \cdot {}_2F_1 \left( u + \frac12,v + \frac12,\frac32;1 - ch^2 \left( \fracx\gamma \right) \right)} \right],$$ (21) $$ \varepsilon = \frac(\lambda - 1 - n)^2 \gamma^2 + \frac\pi^2 n^2 L^2 + \frac\lambda (\lambda - 1)\gamma^2 , $$ (22)where \( u = \frac12(\lambda - \gamma k) \) and \( v = \frac12(\lambda + \gamma k), \) C 1 and C 2 are normalization constants, \( {}_2F_1 \left( a,b,c;x AMN-107 chemical structure \right) \) is the hypergeometric function. For small values of the coordinate x, the potential (17) takes the form $$ V_\textPT (x) \approx \frac\pi^2 n^2 L^2 + \frac\lambda (\lambda - 1)x^2 \gamma^4 . $$ (23) Further, solution to the Schr?dinger equation for the ��slow�� subsystem with the potential (23) is completely similar to the procedure with parabolic potential considered above. As a result, we IAP inhibitor arrive at the following expression for the equidistant energy spectrum of a CC: $$ \varepsilon = \alpha_n + \frac2\sqrt \lambda (\lambda - 1) \gamma^2 \left( N + \frac12 \right),\quad N = 0,1,2, \ldots $$ (24)which perfectly agrees with the result (16). Direct Interband Light Absorption Now, we consider direct interband light absorption by CQD with thin falciform cross section, in the strong SQ regime. This means that the conditions \( L \ll \left\ a_\textB^\texte ,a_\textB^\texth \right\ \) are satisfied, where \( a_\textB^\texte(\texth) \) is an effective Bohr radius of the electron (or the hole). We consider the case of a heavy hole, when \( m_\texte \ll m_\texth , \) with m e and m h being the effective masses of the electron and hole, respectively. Under conditions of one-electron band theory approximation, the absorption coefficient is given by the expression [13]: $$ K = A\sum\limits_\nu ,\nu^\prime ^2 \delta \left( \hbar \Upomega - E_\textg - E_\nu ^\texte - E_\nu^\prime^\texth \right), $$ (25)where �� and �͡� are sets of quantum numbers corresponding to the electron and heavy hole, E g is the forbidden gap width in the bulk semiconductor, �� is the incident light frequency, and A is a quantity proportional to the square of matrix element in decomposition over Bloch functions.