(a) Current density is ultimately determined by conservation of charge. If we define n=4*4 then show...

 

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(a) Current density is ultimately determined by conservation of charge. If we define n=4*4 then show using the Schrodinger equation that the current density operator y.ddv.) dr dr J satisfies the continuity equation for charge, dn dt h 2mi (b) For a plane wave interpret the result [5 pts] which represents charge conservation (increasing charge implies influx, i.e., negative gradient, of current). Note that you should be able to derive this equation solely by using Schrödinger equation for the wavefunction V, and complex conjugating the entire equation to get an equation for . [10 pts] Voeika, simplify the current expression and = dJ dr (c) If instead we use the ground state solution for a particle in a box, V Vo sin kr, what is the current density? What does that mean? [5 pts] (a) Current density is ultimately determined by conservation of charge. If we define n=4*4 then show using the Schrodinger equation that the current density operator y.ddv.) dr dr J satisfies the continuity equation for charge, dn dt h 2mi (b) For a plane wave interpret the result [5 pts] which represents charge conservation (increasing charge implies influx, i.e., negative gradient, of current). Note that you should be able to derive this equation solely by using Schrödinger equation for the wavefunction V, and complex conjugating the entire equation to get an equation for . [10 pts] Voeika, simplify the current expression and = dJ dr (c) If instead we use the ground state solution for a particle in a box, V Vo sin kr, what is the current density? What does that mean? [5 pts]

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dn dt from it 24 76 uu dy dt st Schrdingers equation X As 2... View the full answer