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Chapter 35: Problem 2

Does quantum tunneling violate energy conservation? Explain.

Short Answer

Expert verified
No, quantum tunneling does not violate energy conservation. The particle does not gain or lose energy during its tunneling process. The misconception arises from a classical viewpoint; in quantum mechanics, the total energy of the system remains conserved even during quantum tunneling.

Step by step solution

01

Understanding Quantum Tunneling

Quantum tunneling is not a phenomenon that one would encounter in the classical world. In the realm of quantum mechanics, it is possible for particles to pass through potential barriers, even if their energy is less than the potential energy barrier. This is known as quantum tunneling. This tunneled particle seems to be suddenly appearing on the other side of the potential barrier without having traversed it, thereby apparently violating the principle of energy conservation of classical physics.
02

Conservation of Energy in Quantum Mechanics

In quantum mechanics, the principle of energy conservation is not violated by quantum tunneling. Energy is not created or destroyed even in quantum tunneling, the particle doesn鈥檛 gain or lose energy when it tunnels through. Before and after the tunneling phenomenon, the total energy of the wave-particle remains the same. Therefore, quantum tunneling does not violate energy conservation.
03

Reason behind this misconception

The misconception arises from our classical view of energy barriers. In classical mechanics, an object with less energy than the barrier cannot pass through it. In quantum mechanics, however, it is the probability of finding a particle at a particular location that is important. Even if the probability decreases exponentially as the energy difference increases, there is still a non-zero probability that the particle can appear on the other side of the barrier. This is why particles can tunnel through energy barriers in quantum mechanics, without gaining or losing energy.

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Most popular questions from this chapter

A particle is in the \(n\) th quantum state of an infinite square well. (a) Show that the probability of finding it in the left-hand quarter of the well is $$ P=\frac{1}{4}-\frac{\sin (n \pi / 2)}{2 n \pi} $$ (b) Show that for odd \(n\), the probability approaches the classical value \(\frac{1}{4}\) as \(n \rightarrow \infty\)

Find an expression for the normalization constant \(A\) for the wave function given by \(\psi=0\) for \(|x|>b\) and \(\psi=A\left(b^{2}-x^{2}\right)\) for \(-b \leq x \leq b\)

Determine the ground-state energy for an electron in an infinite square well of width \(10.0 \mathrm{nm}\)
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