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4. We can always write the wavefunction as V = V₁ +iV₂ where V₁ and ₂ are real functions. Using the one-dimensional free particle Schrodinger equation, what equations should ₁ and ₂ satisfy?

4. We can always write the wavefunction as V = V₁ +iV₂ where V₁ and ₂ are real functions. Using the one-dimensional free particle Schrodinger equation, what equations should ₁ and ₂ satisfy?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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3. The free particle Schrodinger equation describes a non-relativistic matter wave without forces (no potential energy). Remember, when we considered plane wave solutions, the Schrodinger equation was consistent with the non-relativistic energy of a free particle: E = p²/2m. Now let's try finding a relativistic wave equation! To do this, start with a plane wave with the form Ų = e²(kx-wt) where k = p/ħ and w = E/ħ and try to find a differential equation that yields the correct relativistic energy expression when applied to this plane wave. It will be useful to consider the relativistic energy squared: E² = p²c² + m²c². 1 4. We can always write the wavefunction as V = V₁ +iV₂ where V₁ and ₂ are real functions. Using the one-dimensional free particle Schrodinger equation, what equations should ₁ and ₂ satisfy?
Transcribed Image Text:3. The free particle Schrodinger equation describes a non-relativistic matter wave without forces (no potential energy). Remember, when we considered plane wave solutions, the Schrodinger equation was consistent with the non-relativistic energy of a free particle: E = p²/2m. Now let's try finding a relativistic wave equation! To do this, start with a plane wave with the form Ų = e²(kx-wt) where k = p/ħ and w = E/ħ and try to find a differential equation that yields the correct relativistic energy expression when applied to this plane wave. It will be useful to consider the relativistic energy squared: E² = p²c² + m²c². 1 4. We can always write the wavefunction as V = V₁ +iV₂ where V₁ and ₂ are real functions. Using the one-dimensional free particle Schrodinger equation, what equations should ₁ and ₂ satisfy?
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