When is the temporal part of the wave function 0 ? Why is this important?
The likelihood of discovering the probability would be 0 if the temporal part of a wave function was zero, implying that the particle would have vanished.
The wave function itself has no physical significance. However, the amplitude of wave function corresponds to and the square of the wave function relates to the photon density, the number of photons present in a region, it relates to electron density in a certain region.
Therefore, using the square of wave function, we can measure of the probability that the electron can be found within a particular tiny volume of the atom.
Hence, The likelihood of discovering the probability would be 0 if the temporal part of a wave function was zero, implying that the particle would have vanished.
Quantum-mechanical stationary states are of the general form . For the basic plane wave (Chapter 4), this is , and for a particle in a box it is . Although both are sinusoidal, we claim that the plane wave alone is the prototype function whose momentum is pure-a well-defined value in one direction. Reinforcing the claim is the fact that the plane wave alone lacks features that we expect to see only when, effectively, waves are moving in both directions. What features are these, and, considering the probability densities, are they indeed present for a particle in a box and absent for a plane wave?
In Section 5.5, it was shown that the infinite well energies follow simply from the formula for kinetic energy, p2/2m; and a famous standing-wave condition, . The arguments are perfectly valid when the potential energy is 0(inside the well) and L is strictly constant, but they can also be useful in other cases. The length L allowed the wave should be roughly the distance between the classical turning points, where there is no kinetic energy left. Apply these arguments to the oscillator potential energy, .Find the location x of the classical turning point in terms of E; use twice this distance for L; then insert this into the infinite well energy formula, so that appears on both sides. Thus far, the procedure really only deals with kinetic energy. Assume, as is true for a classical oscillator, that there is as much potential energy, on average, as kinetic energy. What do you obtain for the quantized energies?
Because protons and neutrons are similar in mass, size, and certain other characteristics, a collective term, nucleons, has been coined that encompasses both of these constituents of the atomic nucleus. In many nuclei, nucleons are confined (by the strong force, discussed in Chapter) to dimensions of rough femtometers. Photons emitted by nuclei as the nucleons drop to lower energy levels are known as gamma particles. Their energies are typically in the Me range. Why does this make sense?
A particle is described by the wave function
(a) Show that the normalization constant is correct.
(b) A measurement of the position of the particle is to be made. At what location is it most probable that the particle would be found?
(c) What is the probability per unit length of finding the particle at this location?
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