Calculation of transition energies in excited state solutions of quantum dots

Recently, thanks to rapid developments in technology, it has become possible to produce low-dimensional structures defined as nanometer (nm) scale two-dimensional (quantum wells), one-dimensional (quantum wires) and zero-dimensional (quantum dots) quantum mechanical systems. Low-dimensional structures have a wide range of applications, such as their use in the construction of transistors, sensors, lasers and photodetectors. Developing, understanding and controlling these structures will be critical for technological innovations in the fields of nanotechnology and materials science. However, quantum transition energies play an important role in determining the optical and electronic properties of low-dimensional structures. Quantum transition energies express the energy required or released by a particle during its transition from one energy level to another in a quantum system. These transitions are described by the fundamental principles of quantum mechanics, and the difference between the energy levels determines the transition energy. Therefore, the main purpose of the study is to define the hamiltonian, subband and impurity atom wave functions of the system for the ground state (1s) and excited state (1p) in the spherical quantum dot under the effective mass approximation and to find the binding energies using the variation method. Transition energies, defined as the difference between ground and excited state binding energies, depending on the radius of the quantum dot, were calculated for different aluminum concentrations and temperature values. This study, which is planned to reveal the relationship between subband and impurity transition energies with aluminum concentration and temperature, will be a source for experimental and theoretical studies on similar systems.