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6.007 Lecture 38: Examples of Heisenberg
6.007 Lecture 38: Examples of Heisenberg

... Measuring Position and Momentum of an Electron • By Planck’s law E = hc/λ, a photon with a short wavelength has a large energy • Thus, it would impart a large ‘kick’ to the electron ...
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... Are they talking about its mass or how much it weighs? Why does it matter? b. If the rock were on the Moon instead of the Earth, would they still refer to it as a “10 kilogram rock”? ...
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... source of the oscillations (your hand), you will notice that the rope is executing the same type of motion as the source except for the phase of the motion, where phase is defined as a fraction of a complete cycle from a specified reference, often expressed as an angle. You see in Figure 16.2 that t ...
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Wave packet



In physics, a wave packet (or wave train) is a short ""burst"" or ""envelope"" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere. Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no dispersion, see figure) or it may change (dispersion) while propagating.Quantum mechanics ascribes a special significance to the wave packet; it is interpreted as a probability amplitude, its norm squared describing the probability density that a particle or particles in a particular state will be measured to have a given position or momentum. The wave equation is in this case the Schrödinger equation. It is possible to deduce the time evolution of a quantum mechanical system, similar to the process of the Hamiltonian formalism in classical mechanics. The dispersive character of solutions of the Schrödinger equation has played an important role in rejecting Schrödinger's original interpretation, and accepting the Born rule.In the coordinate representation of the wave (such as the Cartesian coordinate system), the position of the physical object's localized probability is specified by the position of the packet solution. Moreover, the narrower the spatial wave packet, and therefore the better localized the position of the wave packet, the larger the spread in the momentum of the wave. This trade-off between spread in position and spread in momentum is a characteristic feature of the Heisenberg uncertainty principle,and will be illustrated below.
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