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Differential Equations: These are equations involving derivatives of a function. In this chapter, ordinary differential equations with one independent variable are discussed, as well as linear and nonlinear differential equations 1. Boundary Conditions: These are conditions that specify the value of a function or its derivatives at specific points. They are used to determine the constants in the general solution of a differential equation 1. Linear Differential Equation: A type of differential equation where the dependent variable and its derivatives appear to the first power and are not multiplied together 1. Nonlinear Differential Equation: A differential equation that cannot be written in the form of a linear differential equation. It involves terms where the dependent variable or its derivatives appear to a power other than one or are multiplied together 1. Homogeneous Differential Equation: A linear differential equation where the function on the right-hand side is zero 1. Inhomogeneous Differential Equation: A linear differential equation where the function on the right-hand side is not zero 1. Schrödinger Equation: A fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time. The time-independent Schrödinger equation is used in this chapter to solve for the stationary-state wave functions and energy levels of a particle in a one-dimensional box 1. Wave Function (ψ): A mathematical function that describes the quantum state of a particle. The square of the wave function's magnitude gives the probability density of finding the particle at a given position 1. Quantum Number (n): A number that quantizes the energy levels of a particle in a box. Each quantum number corresponds to a different wave function and energy state 1. Nodes: Points where the wave function is zero. The number of nodes increases with the quantum number 1. Ground State: The lowest energy state of a particle in a box. It corresponds to the quantum number n=1 1. Excited States: Energy states higher than the ground state. They correspond to quantum numbers n=2, 3, etc 1. Bohr Correspondence Principle: A principle stating that the predictions of quantum mechanics converge to those of classical mechanics as the quantum numbers become very large 1. Orthogonality: A property of wave functions where the integral of the product of two different wave functions over all space is zero 1. Normalization: The process of adjusting the wave function so that the total probability of finding the particle is one 1. Tunneling: A quantum mechanical phenomenon where a particle can pass through a potential energy barrier that it classically should not be able to pass 1.