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Examination of the Amplitude Equation to the Characteristics of Harmonic Oscillators: The Concept of Schrodinger Wave Equation

C. P Ukpaka

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 equation

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References


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