Lecture note7 - Delta Ftn Pot, Finite Sq Well

Lecture note7 - Delta Ftn Pot, Finite Sq Well - 101/2...

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x 0 0 0 Ψ (x) (real part) V(x) Ψ (x) (real part) Ψ (x) (real part) V(x) V(x) (a) (b) (c) Here are some realistic numerical simulations for a given potential, V(x), and energy, E, as opposed to rough sketches that may suffer from scale problems and unintended errors. E E E Note that in all cases, the wave length becomes shorter when E V(x) becomes large, i.e. in the well region . This is an important point to remember. However, the amplitude is not necessarily larger in the well region . (A few students said in the midterm that the amplitude should be larger in the well than outside of it.) In order to see why, let us first consider the well and the free space (on the left) as being completely separate. I.e., we can make the barrier so high that there is no tunneling between the two regions. Notice that within the well, we are talking about bound states, and so E is quantized, while in the free space, E is not quantized. Now consider lowering the barrier.
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Lecture note7 - Delta Ftn Pot, Finite Sq Well - 101/2...

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