The solution of the Schrodinger equation to the left of the step in the range x < 0 , to the right of the step in the range x > 0 .

Question

8 Two moving charged particles exert forces on each other because each creates a magnetic field that acts on the other. These two "Lorentz" forces are proportional to vix (2 xr) and 2 x (vi x-r), where is the vector between the particle positions. Show that these two forces are equal and opposite in accordance with Newton's third law if and only if rx (vi × 2) = 0.

Answer 1

Question

Chapter 7, Problem 2P

(a)

To determine

The solution of the Schrodinger equation to the left of the step in the range x<0, to the right of the step in the range x>0.

(b)

To determine

The expression for reflection coefficient in this case and prove that it can be written in this form: R=(k1−k2)2(k1+k2)2 . The expression for transmission factor using the sum rule obeyed by these coefficients.

(c)

To determine

The value of R and T in the limiting cases of E→U and E→∞ .

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8 Two moving charged particles exert forces on each other because each creates a magnetic field that acts on the other. These two "Lorentz" forces are proportional to vix (2 xr) and 2 x (vi x-r), where is the vector between the particle positions. Show that these two forces are equal and opposite in accordance with Newton's third law if and only if rx (vi × 2) = 0.

6 The force = +3 + 2k acts at the point (1, 1, 1). Find the torque of the force about (a) (b) the point (2, -1, 5). Careful about the direction of ŕ between the two points. the line = 21-+5k+ (i-+2k)t. Note that the line goes through the point (2, -1, 5).

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