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A particle of mass m and energy E, moving in the positive x-direction, encounters a one dimensional potential barrier at x = 0. The barrier is defined by
V = 0 for x < 0
V = V0 for x > 0 (E > V0)
If the wave function of the particle in the region x < 0 is given as Aeikx + Be-ikx
If B/A = 0.4, then find E/V0 .
V = 0 for x < 0
V = V0 for x > 0 (E > V0)
If the wave function of the particle in the region x < 0 is given as Aeikx + Be-ikx
If B/A = 0.4, then find E/V0 .
Correct answer is '1.225'. Can you explain this answer?
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To solve this problem, we need to consider the behavior of the particle as it encounters the potential barrier.
1. Before the barrier (x < />
Since the particle is moving in the positive x-direction, it has kinetic energy E. The potential energy V is 0, so the total energy of the particle is E. We can write this as:
E = KE + V = E + 0 = E
2. Inside the barrier (0 < x="" />< />
Inside the barrier, the potential energy V is given by V = -V0, where V0 is a positive constant. The total energy of the particle is still E, so we can write:
E = KE + V
E = KE - V0
KE = E + V0
3. After the barrier (x > a):
After the barrier, the potential energy V is 0 again. The total energy of the particle is E, so we can write:
E = KE + V
E = KE + 0
KE = E
From the above equations, we can see that the kinetic energy of the particle changes as it encounters the barrier. Inside the barrier, the kinetic energy decreases by an amount equal to the potential energy of the barrier (V0).
This change in kinetic energy can be understood as the particle losing energy to overcome the potential barrier. The amount of energy lost depends on the height of the barrier (V0).
Note: The above analysis assumes that the particle is a non-relativistic particle. If the particle is a relativistic particle, additional considerations need to be taken into account.
1. Before the barrier (x < />
Since the particle is moving in the positive x-direction, it has kinetic energy E. The potential energy V is 0, so the total energy of the particle is E. We can write this as:
E = KE + V = E + 0 = E
2. Inside the barrier (0 < x="" />< />
Inside the barrier, the potential energy V is given by V = -V0, where V0 is a positive constant. The total energy of the particle is still E, so we can write:
E = KE + V
E = KE - V0
KE = E + V0
3. After the barrier (x > a):
After the barrier, the potential energy V is 0 again. The total energy of the particle is E, so we can write:
E = KE + V
E = KE + 0
KE = E
From the above equations, we can see that the kinetic energy of the particle changes as it encounters the barrier. Inside the barrier, the kinetic energy decreases by an amount equal to the potential energy of the barrier (V0).
This change in kinetic energy can be understood as the particle losing energy to overcome the potential barrier. The amount of energy lost depends on the height of the barrier (V0).
Note: The above analysis assumes that the particle is a non-relativistic particle. If the particle is a relativistic particle, additional considerations need to be taken into account.
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A particle of mass m and energy E, moving in the positive x-direction, encounters a one dimensional potential barrier at x = 0. The barrier is defined byV = 0 for x < 0V = V0 for x > 0 (E > V0)If the wave function of the particle in the region x < 0 is given as Aeikx+ Be-ikxIf B/A = 0.4,then find E/V0.Correct answer is '1.225'. Can you explain this answer?
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