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Start Free Sprint →Focus on 5 Core Modules: (1) Quantum Mechanics (Wave function physical significance, Born interpretation, Normalization, 1D Schrödinger equation derivation, Particle in an infinite potential well discrete energy eigenvalues & numericals); (2) Quantum Computing (Qubit, Quantum Entanglement, Quantum Parallelism, Pauli-X matrix representation, Quantum Key Distribution - QKD BB84); (3) Lasers & Optical Fibers (Spontaneous vs Stimulated emission, Nd:YAG 4-level laser energy level diagram, Optical fiber loss mechanisms and attenuation); (4) Semiconductor Physics & Devices (Hall Effect & Hall Voltage derivation, Fermi-Dirac distribution & Fermi level occupation probability, Photodiode vs Solar Cell comparison, LED working principle); (5) Nanoscience & Thin Films (Ball milling nanomaterial synthesis, Top-down vs Bottom-up approaches, Advantages of thin films over bulk materials, Sputtering deposition technique).
Key Points: Boundary conditions: psi(0) = 0 and psi(L) = 0. Solution inside well psi(x) = A sin(kx) + B cos(kx). At x=0, B=0. At x=L, sin(kL)=0 => kL = n*pi => k = n*pi/L. Energy E = (hbar^2 * k^2)/(2m) = (n^2 * h^2)/(8 * m * L^2). Normalization integral integral_0^L |psi|^2 dx = 1 gives A = sqrt(2/L).
Key Points: Qubit |psi> = alpha |0> + beta |1> with |alpha|^2 + |beta|^2 = 1. Pauli-X matrix = [[0, 1], [1, 0]]. Action: X|0> = |1>, X|1> = |0> (Quantum NOT). QKD (BB84 protocol): Alice transmits single photons randomly polarized across rectilinear (+) and diagonal (x) bases, Bob measures in random bases, public basis reconciliation creates provably secure symmetric key.
Key Points: Draw 4 energy levels: Ground State (4I9/2), Pump Bands (4F5/2, 4H9/2), Metastable Upper Lasing State (4F3/2), and Lower Lasing State (4I11/2). Optical pumping with flashlamp/laser diode causes excitation followed by fast non-radiative decay to 4F3/2. Stimulated emission yields 1064 nm IR laser radiation, followed by fast relaxation to ground state.
Key Points: Equate Lorentz magnetic force q*v_d*B to electric force q*E_H => E_H = v_d*B. Current density J = n*q*v_d => v_d = J/(n*q). Hall Voltage V_H = E_H * w = (B * I) / (n * q * t). Hall coefficient R_H = 1/(n*q). Sign of V_H indicates p-type (+ve) or n-type (-ve).
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