Examination of the Amplitude Equation to the Characteristics of Harmonic Oscillators: The Concept of Schrodinger Wave Equation
Abstract
Although Heisenberg’s matrix mechanics was developed first, the Schrödinger equation was the first useful quantum wave equation. However, the Schrödinger equation is applicable only to non-relativistic cases. As opposed to classical physics, where the wave equation can be derived from first principles, in quantum physics the wave equation is obtained by a plausibility argument based on classical physics and the de Broglie hypotheses. Inserting the de Broglie relations. A frequently encountered problem is where the potential is time independent, for which the quantized energy solutions are time independent. For such cases the right-hand side of the time-dependent Schrödinger equation is a function of only the spatial coordinates while the left-hand side is a function only of time. For such a system the two sides are independent and the spatial and time parts of the wave function can be separated. Key words: Examination, amplitude Equation, characteristics, harmonic oscillators, concept, schrodinger, wave equationReferences
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