Regarding the verification of passing a module in quantum mechanics for TUM Quantum Science and Technology Masters application.

Hi everyone. I am an applicant for this year's winter semester at the QST Masters Program at TUM. I have a bachelor's in electrical engineering and I have attached the contents of pages of the document I submitted for verification of passing a module in quantum mechanics.

I would request you to check them and give your assessment whether they would suffice as evidence for completing a module in quantum mechanics. Thank you.

Subject: Documents for Verification of successful completion of a module in quantum mechanics In the following pages of this document, I am submitting the following documents to support the review of my background for the Quantum Mechanics prerequisite:

1. University course syllabi and relevant transcript entries from my degree program.

2. MITx online certificates in Mastering Quantum Mechanics and Applications of Quantum Mechanics.

3. Physics GRE score evidence, including my score of 81% in the Quantum Mechanics and Atomic Physics section. Syllabus of Quantum Mechanics for the Physics GRE.

My academic preparation includes physics coursework in atomic structure, semiconductor physics, energy bands, carrier statistics, and related topics, together with MITx quantum mechanics coursework and a strong Physics GRE result in the relevant section. I submit these materials for curricular review as evidence of substantial preparation in Quantum Mechanics and related topics.

Relevant Courses during undergrad:

1. Phy 4121: Engineering Physics I-

Content Covered: Atomic structure. Thompsons, Rutherford and Bhor’s atomic model. Atomic arrangement in solids. Different types of bonds in solids- metallic, Vander Walls and ionic bond. Electronic structure of materials: Free electron the theory, Metallic conduction. Energy bands, Brillouin zones, Temperature dependence of metallic conductivity. Semiconductors: Band theory, intrinsic and extrinsic semiconductors, Fermi levels, mobility and electrical conductivity, carrier diffusion and life time, P-N junction, biasing conditions, V-I characteristics, effects of temperature on diode characteristics. Magnetic materials: Properties, Dia-, Para- and Ferromagnetism, Hysteresis loop, B-H curve, Energy losses in magnetic materials and their measurements. Soft and hard magnetic materials, ferrities. Optics: Interference. Young’s double slit experiment, fringe width, determination of wavelength of light and thickness of a transparent sheet. Interference due to reflection. Newton’s ring. Determination of refractive index of a liquid. Fresnel and Fraunhoffer diffraction through single slit. Intensity of diffracted beam. Polarization: Polarized and Non-polarized light. Light polarization by reflection. Double refraction, Malus law, Intensity of polarized light. Photoelectricity: Laws of photoemission and Einstein’s equation. Photoelectric cell and its use. Introduction to superconductivity and its application.

Reference: IUT EEE Syllabus ( https://eee.iutoic- dhaka.edu/uploads/pdf/1739898350_1782.pdf ) Page:79-80

2. Phy 4221: Engineering Physics II-

Content Covered: Structure of matter: Classification of Solids; Crystalline and noncrystalline solids; unit cell, Crystal systems, Crystal structures, Atomic radius and crystal packing and packing density. Crystal directions, Planes 84 and Planar spacing and cell edge. Bragg’s law. Deflects in Solids: Frankel and Schottky deflects; Diffusion in solids. Modern Physics: Special theory of relativity, Galilean relativity, Lorentz transformation equations, relativistic length, time and mass. Mass energy relation. Photo-electric effect. Compton scattering. Radioactivity. Radioactive decay law. Half-lifes, mean life. Introduction to Nuclear fission and fusion. Nuclear power plant. Thermal electricity: Thermocouple, Seebeck effect, Peltier and Thompson effect, Thermo-emf. Wave and oscillation: Simple harmonic motion, damped simple harmonic oscillations, forced oscillations, resonance vibrations of membranes and columns. Combination and composition of simple harmonic motions, Lissajous’ figures. Transverse and longitudinal nature of waves, travelling and standing waves, intensity of wave, energy calculation of progressive and stationary waves, phase velocity, group velocity. Sound waves: velocity of longitudinal wave in a gaseous medium. Doppler effect. Architectural acoustics: Sabine’s formula, requisites of a good auditorium

Reference: IUT EEE Syllabus ( https://eee.iutoic- dhaka.edu/uploads/pdf/1739898350_1782.pdf ) Page:83-84

3. EEE 4409: Semiconductor Physics-

Content Covered: Energy bands in semiconductor, Carrier statistics and Fermi level, carrier concentrations at equilibrium, temperature dependence of carrier concentrations, conductivity and mobility, effects of temperature and doping on mobility, high field effect, Hall effect, invariance of Fermi level. Carrier lifetime, direct and indirect recombination, quasi-Fermi level, photoconductive devices, Drift and diffusion of carriers, continuity and diffusion equations. PN junction contact potential, equilibrium Fermi level, space charge, forward and reverse bias, carrier injection, minority and majority carrier currents, avalanche and zener breakdown, time variation of stored charge, reverse recovery transient and capacitance. Metal-semiconductor junctions: Schottky barriers, rectifying and ohmic contacts. Bipolar Junction Transistor: Basic principle of pnp and npn transistors, emitter efficiency, base transport factor and current gain, diffusion equation in the base, terminal currents, coupled-diode model and charge control analysis. 92 MOSFET: capacitance, energy band diagrams and flat band voltage, threshold voltage analysis and control, static C-V characteristics, MOSFET operation, I-V relationship and body effect. Optoelectronic devices: Photo diodes. Light Emitting Diodes: Visible and infrared LED, principle, material. Semiconductor Laser.

Reference: IUT EEE Syllabus ( https://eee.iutoic- dhaka.edu/uploads/pdf/1739898350_1782.pdf ) Page:91-92

In the rest of the document, I shared my 2 MITx certificates on "Mastering Quantum Mechanics (based on MIT's course 8.05 taught by Barton Zwiebach)" and "Applications of Quantum Mechanics (based on MIT's course 8.06 taught by Barton Zwiebach)" and the Physics GRE transcript showing that I scored 81% in the QM and Atomic Physics Section.

Thank you for reading this long post. I genuinely appreciate your help.