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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 the principle of energy conservation. The particle's energy does not alter during the tunneling process, so energy is neither created nor destroyed.

Step by step solution

01

Review the principle of energy conservation

This principle is a fundamental concept in physics that dictates that energy cannot be created or eliminated, only transferred from one form to another or converted between forms.
02

Understand Quantum Tunneling

Quantum tunneling is a quantum mechanical phenomenon where a particle can pass through an energy barrier it could not, classically. It occurs due to the wave-like nature of particles in quantum mechanics, and their associated wavefunctions, which can non-zero probabilities for particles to exist on the 'other side' of an energy barrier.
03

Correlate the two concepts

Despite appearances, quantum tunneling does not violate the principle of energy conservation. While a particle can 'tunnel' past an energy barrier it theoretically cannot surmount, the energy of the particle doesn't actually change in the process. Rather, the quantum nature of the particle allows it to exist in a superposition of states, including potentially being on the 'other side' of the energy barrier. When the particle is observed, it may appear on the other side of the energy barrier without having had enough energy to get there, but at no point was energy created or destroyed.

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Most popular questions from this chapter

What's the quantum number for a particle in an infinite square well if the particle's energy is 25 times the ground-state energy?

A particle is confined to a 1.0 -nm-wide infinite square well. If the energy difference between the ground state and the first excited state is \(1.13 \mathrm{eV},\) is the particle an electron or a proton?

An infinite square well extends from \(-L / 2\) to \(L / 2 .\) (a) Find expressions for the normalized wave functions for a particle of mass \(m\) in this well, giving separate expressions for even and odd quantum numbers. (b) Find the corresponding energy levels.

You're trying to convince a friend that nuclear energy represents a much more concentrated energy source than fossil fuels, whose combustion involves rearranging atomic electrons. For a rough comparison, you calculate the ground-state energy of a proton confined to 1 -fm-diameter atomic nucleus and that of an electron confined to a 0.1 -nm-diameter atom. Approximating each system as a one-dimensional infinite square well, what's the ratio of their ground-state energies?

The ground-state wave function for a quantum harmonic oscillator has a single central peak. Why is this at odds with classical physics?
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