what is the probability that the particle will be reflected?

Question

(169) when a particle approaching a potential step has a total energy that is greater than the potential step, what is the probability that the particle will be reflected?

a) p < 0 

b) p = 0 

c) p = 1 

d) p > 0 

e) p = ∞why the answer is D not E?thx

Answer 1

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Have you read the question correctly?

Answers a) and e) must both be wrong because probability is, by definition, a value between 0 and 1.

Imagine a 1kg ball rolling towards an uphill ramp of height 2m.  To reach the top of the ramp, the ball must have at least (mgh = 1*10*2 =) 20J of initial kinetic energy.

In a classical system if the ball's kinetic energy is less than 20J, the ball won't reach the top of the ramp, it will roll back - it will be 'reflected'.

In a classical system if the ball's kinetic energy is more than 20J, the ball will reach the top of the ramp and continue rolling (though slower).

In a quantum system, if the ball's kinetic energy is less than 20J, the ball *STILL* has a small probability of going up the ramp (basically quantum tunnelling).

And in a quantum system, if the ball's kinetic energy is more than 20J, the ball *STILL* has a small probability of being 'reflected' by the ramp..  This last situation is what the question is about.  So the answer is d).