Knowing that we need to solve a 2nd-order differential equation in the time-independent Schrödinger Equation, we shall write the solutions here, based on which form the equation takes. For an in-depth study, check out www.gaussianmath.com
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QM0.1: Postulates of Quantum Mechanics
QM0.2: Time Evolution of a system
QM0.3: Time-Independent Schrödinger Equation
QM0.4: "Square" Potentials
QM0.5: Bound States - Properties of one-dimensional motion
QM0.6: Unbound States - Properties of one-dimensional motion
QM0.7: Solutions to the 2nd-order Differential Equation
QM0.8: General Approach in solving problems
QM0.9: Wave solutions and Energy levels
QM0.10: Continuity and Boundary Conditions
QM0.11: Physical Meaning of Wave solutions
QM0.12: Stationary States