Given in fig are examples of some potential energy functions in one dimension. The total enrgy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any, in which the particle cannot be found for the given energy. Also, indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.

Explanation

(a) For ` x gt a ` ,
P.E `gt ` Total Energy
Hence K.E is negative which is not possible .
Therefore , particle cannot exist in the region .
In the region ` x lt a ` , the minimum energy the particle can have is when it is at rest , that is its kinetic energy is zero . Also we see that the potential energy for this region is also zero . Thus , minimum total energy is zero .
Therefore particle cannot exist in this region .
(b ) For every region , the potential energy is greater than teh total energy and hence K.E is negative which is not possible , Hence , particle cannot be found in any region .
The minimu energy of the particle is `V_(1)` , when it is at x = 0
(c ) As the potential energy is lesser tha the total energy in the region ` a lt x lt b ` . Therefoore , the particle cannot exist in this region ` x lt a ` and ` x gt b ` .
The minimum energy of the aprticle is `V_(1)`
(d) For ` - b/2 lt x - a/2 and a/2 lt x lt b/2 `, P.E `gt E ` ( total energy )
K.E is negative . the particle cannot be found in these regions . The minimum energy of the particle is ` - V_(1)` .