How can expectation of position^2 be > L

Thread starter NucEngMajor
Start date Nov 12, 2015
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In summary, the conversation discusses the expectation of position squared being greater than the length of a position, which is a result of the uncertainty principle in quantum mechanics. This principle explains that it is impossible to know the exact position and momentum of a particle simultaneously. It applies to all particles and is related to the concept of wave-particle duality, where particles can exhibit both wave-like and particle-like behaviors. This means that the exact position of a particle cannot be known with certainty, leading to the expectation value of position squared being larger than the length of a position.

Nov 12, 2015

NucEngMajor

How can position^2 expectation be greater than the Length of "box"? I mean <x^2> = L^2 / 3. Say L=100m then we have <x^2> = 333m. How is this possible?

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Nov 12, 2015

andrewkirk

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Why should it not be possible? After all, ##100^2>100##. In any case the square is not comparable to the length, as the units of one is square metres and of the other is only metres. The volume of a cube that is 10cm per side is more than 10 ##cm^3##.

FAQ: How can expectation of position^2 be > L

1. How is expectation of position squared greater than the length of a position?

The expectation of position squared being greater than the length of a position is a result of the uncertainty principle in quantum mechanics. This principle states that it is impossible to know the exact position and momentum of a particle at the same time.

2. Can you provide an example of how expectation of position squared can be greater than the length of a position?

One example is the case of a free particle in a one-dimensional box. In this scenario, the expectation value of position squared is equal to the length of the box squared, which is greater than the length of the box itself.

3. How does the uncertainty principle explain the expectation of position squared being greater than the length of a position?

The uncertainty principle states that the more precisely we know the position of a particle, the less precisely we know its momentum, and vice versa. This means that the expectation value of position squared can be larger than the length of a position due to the inherent uncertainty in the measurement of position and momentum.

4. Is this phenomenon limited to certain situations, or does it apply to all particles?

The uncertainty principle applies to all particles, including atoms, molecules, and subatomic particles. It is a fundamental principle in quantum mechanics and plays a crucial role in understanding the behavior of matter at a microscopic level.

5. How does the concept of wave-particle duality contribute to the expectation of position squared being greater than the length of a position?

The concept of wave-particle duality states that particles can exhibit both wave-like and particle-like behaviors. This means that the exact position of a particle cannot be known with certainty, as it is described by a wave function that can spread out over a range of positions. Therefore, the expectation value of position squared can be larger than the length of a position due to the probabilistic nature of the particle's position.