Chapter 1: Problem 10

State Heisenberg's uncertainty principle and discuss its significance.

Short Answer

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Heisenberg's Uncertainty Principle states that the position and momentum of a particle cannot be both exactly measured at the same time. The more precisely one measures position, the less precise the measurement of momentum becomes, and vice versa. This principle signifies the inherent 'fuzziness' in the behavior of particles at quantum scales and leads to various counter-intuitive phenomena, such as quantum tunneling.

Step by step solution

State Heisenberg's Uncertainty Principle

Heisenberg's Uncertainty Principle can be stated as follows: It is impossible to simultaneously precisely measure the exact position and momentum of a particle. In essence, the more precisely the position is known, the less precisely the momentum is known, and vice versa. It is mathematically expressed as \( \Delta x \Delta p \geq \frac {h}{4\pi}\), where \( \Delta x \) and \( \Delta p \) are the uncertainties in position and momentum respectively, and \( h \) is Planck's constant.

Discuss the Significance of Heisenberg's Uncertainty Principle

The significance of Heisenberg's Uncertainty Principle lies in the fact that it brings forward the inherent 'fuzziness' or indeterminacy in the quantum world. This fuzziness is not due to the limitations in the measurement instruments, but it is a fundamental aspect of nature at quantum scales. This principle is responsible for various quantum behaviors and phenomena that are counter-intuitive from the perspective of classical physics. An example is quantum tunneling, where a particle can pass through a potential barrier, even if its energy is less than the energy of the barrier.

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State Heisenberg's uncertainty principle and discuss its significance.

Short Answer

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State Heisenberg's Uncertainty Principle

Discuss the Significance of Heisenberg's Uncertainty Principle

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