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intermediary of wave functions it would seem natural to also have at hand a corresponding wave equation to determine how the wave functions evolve through time and space. The Schrödinger wave equation, which serves this purpose, is not something that can be rigorously derived from first principles. Like many other instances in physics,
After the failure of the Bohr atomic model to comply with the Heisenberg’s uncertainty principle and dual character proposed by Louis de Broglie in 1924, an Austrian physicist Erwin Schrodinger developed his legendary equation by making the use of wave-particle duality and classical wave equation.
Schrodinger Wave Equation for a Particle in One Dimensional Box In the first section of this chapter, we discussed the postulates of quantum mechanics i.e. the step-by- step procedure to solve a quantum mechanical problem.
Wave mechanics and the Schr¨odinger equation Although this lecture course will assume a familiarity with the basic concepts of wave mechanics, to introduce more advanced topics in quantum theory, it makes sense to begin with a concise review of the foundations of the subject.
In most cases, one can start from basic physical principles and from these derive partial differential equations (PDEs) that govern the waves. In Section 4.2 we will do this for transverse waves on a tight string, and for Maxwell’s equations describing electromagnetic waves.
In quantum mechanics, particles have wavelike properties, and a particular wave equa-tion, the Schrodinger equation, governs how these waves behave. The Schrodinger equation is di®erent in a few ways from the other wave equations we've seen in this book.
Figure 2.1: Illustration of a plane wave. In free space, the plane wave propagates with velocity cin direction of the wave vector k = (k x,k y,k z). The electric field vector E 0, the magnetic field vector H 0, and k are perpendicular to each other.
