Explain what physicists mean when they say that the de Broglie wavelength relates to the probability...

Explain what physicists mean when they say that the de Broglie wavelength relates to the probability distribution wave function. Please be specific and do not copy and paste previous answers.

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Consider a particle having momentum . According to the wave-particle duality principle each and every object can be described by a wavepocket with a de Broglie wavelength . The momentum and wavelength are related by , where is Planck's constant. Now suppose that in a quantum measurement a particle has a uncertainty in momentum then what is the uncertainty in it's wavelength of the wavepocket or what is the spread in the wavepocket representing the object? Clearly it is which is nothing but the Heisenberg uncertaintly principle, which tells us that the product of the uncertainty in the momentum and location of an object should be always greater than . (Clearly, the concept of uncertainty means that the quantities are given by some probability distribution). In this way the de Broglie wavelength relates to the probability distribution wave function or simply the wavepocket that represents the object which we are talking about.

genius_generous answered 1 year ago

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