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TrickyDicky
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In a QM introductory book , I have read that the wave packet is not a solution of the Schrodinger equation, is this true in some context or is it just an mistake of the author?
Chopin said:It depends on the potential. If there is a potential, then the wave packet is not a solution. If there is no potential, then the Hamiltonian describes a free field, in which case a wave packet is a solution, and the Schrodinger equation describes how the packet moves and spreads out through time. The easiest way to see this is to break the wave packet apart into different energy eigenstates (this is just a Fourier expansion), which are trivial solutions of the SE.
torquil said:Why? The Schrödinger equation is linear also in the presence of a potential, so you can still create a wave packet solution by superposing an infinity of solutions (all solutions if the system with potential of course).
A wave packet is a mathematical concept used in quantum mechanics to describe the behavior of a particle. It represents a localized region of a wave with a finite range of frequencies or wavelengths. In other words, it is a group of waves that travel together and have a specific shape and size.
Exploring the wave packet is important because it helps us understand the behavior of particles at the quantum level. It allows us to study the properties of particles such as position, momentum, and energy, and how they change over time. This insight is crucial in many areas of science, including particle physics and chemistry.
The wave packet is a fundamental concept in quantum mechanics. It is used to describe the wave-like behavior of particles, which cannot be fully understood using classical mechanics. In quantum mechanics, particles are described as both particles and waves, and the wave packet helps us understand how these particles behave as waves.
The critical insight gained from studying the wave packet is that particles at the quantum level do not have a well-defined position or momentum. Instead, they have a probability distribution of being in a certain position or having a certain momentum. This insight challenges our classical understanding of particles and helps us better understand the unpredictable nature of the quantum world.
No, the wave packet itself cannot be observed in real life. It is a mathematical concept used to describe the behavior of particles at the quantum level. However, the effects of the wave packet can be observed through experiments, such as the double-slit experiment, which demonstrate the wave-like behavior of particles.