Two examples illustrating the differences between classical and quantum mechanics

Abstract

Two examples are presented: The first shows that a potential V ( x ) can be in the limit circle case at ∞ even if the classical travel time to ∞ is infinite. The second shows that V ( x ) can be in the limit point case at ∞ even though the classical travel time to infinity is finite. The first example illustrates the reflection of quantum waves at sharp steps. The second example illustrates the tunnel effect.