question4 please 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-relativisticenergy of a free particle: E = p²/2m. Now let's try finding a relativistic wave equation! To do this, start with a planewave with the formŲ =e²(kx-wt)where k =p/ħ and w = E/ħ and try to find a differential equation that yields the correct relativistic energy expressionwhen applied to this plane wave. It will be useful to consider the relativistic energy squared: E² = p²c² + m²c².14. We can always write the wavefunction as V = V₁ +iV₂ where V₁ and ₂ are real functions. Using the one-dimensionalfree particle Schrodinger equation, what equations should ₁ and ₂ satisfy?

Answered: Image /qna-images/answer/8be2d69c-09ee-4f91-938e-3e6254b6a3a2.jpg

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

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter27: Quantum Physics

Section: Chapter Questions

Problem 34P

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Question

question4 please

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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