Consider a particle approaching a finite potential step or inside a potential well. As we know, the particle has a finite probability to penetrate into the region where E < V. The probability remains finite arbitrarily deep into the classically forbidden region. Suppose we set a detector far from the step and wait for a very long time. When we finally detect a particle, what saves the law of conservation of energy?(adsbygoogle = window.adsbygoogle || []).push({});

Unless we have an absolutely crazy potential, the Lagrangian is time-translational invariant, so energy should be conserved. What am I not getting?

The issue was discussed, e.g., here:

physics.stackexchange.com/questions/11188/can-a-particle-be-physically-observed-inside-a-quantum-barrier

I do not think the explanation about the penetration depth is sufficient, since we can set the detector arbitrarily far from the step.

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# Energy conservation in the classically forbidden region

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