By David S. Saxon
In line with lectures for an undergraduate UCLA direction in quantum mechanics, this quantity specializes in the formulation of quantum mechanics fairly than applications. common in either upper-level undergraduate and graduate classes, it bargains a huge self-contained survey instead of in-depth treatments.
Topics contain the twin nature of subject and radiation, kingdom features and their interpretation, linear momentum, the movement of a unfastened particle, Schrödinger's equation, approximation equipment, angular momentum, and lots of different matters. within the pursuits of maintaining the math so simple as attainable, lots of the ebook is restricted to issues of one-dimensional platforms. a variety of one hundred fifty difficulties, a lot of which require lengthy examine, enlarge the text's teachings and an appendix includes recommendations to 50 consultant difficulties. This version additionally encompasses a new creation by way of Joseph A. Rudnick and Robert Finkelstein.
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Extra info for Elementary quantum mechanics
X ~ Ii. p and hall obtain a correspondingly precise inequality. For now, we simply regard each of these quantities as some reasonable measure of the width of a wave packet in configuration and momentum space, respectively. The physical interpretation of this mathematically trivial relation is the following. p and conversely. In other words, the position and momentum of a particle cannot be simultaneously known (or determined or measured) with arbitrary precision, but only within the limits of the relation, equation (56), which is a mathematical, if not yet very accurate, version of the uncertainty principle, first enunciated by Heisenberg.
P is of the order of Ii and is independent of L. For large L, the momentum becomes well defined, the space location poorly defined, and conversely for small L, and always in such a way that the product of the uncertainty in x and that in p is of the order of ~. (b) Gaussian Wave Packet. As a second example, we consider a normalized Gaussian wave packet "'(x) = 'I' vIILV"7r exp [iP()X -~] Ii 2V' (52) which describes a particle localized about the origin within a distance L and with mean momentum Po.
As an example, consider localization of the y-coordinate of a particle by a slit (Figure 3). If the lit has aperture L, 52 LINEAR MOMENTUM p,,------~~ FtGURE 3. Localization of a particle by a slit. iy. ip" = Po sinO = PoO. iy = h, in agreement with the uncertainty principle. A second standard example is the use of a microscope to locate a particle. ix. ix. ix, as the uncertainty principle demands. 7 As implied earlier, it is important to recognize that the uncertainty principal is an integral part of quantum mechanics, as well as a natural and direct consequence of it.
Elementary quantum mechanics by David S. Saxon