2_1_Lecture_2

2_1_Lecture_2 - EE 2 Fall 2007 Class 2 slides 1 Class 2 Outline of lecture Brief summary of the features of quantum mechanics Particle in free

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1 EE 2 Fall 2007 Class 2 slides
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2 Class 2 : Outline of lecture • Brief summary of the features of quantum mechanics • Particle in free space • Particle in a box • Quantization of energy and momentum. • Definition of a quantum state • Density of states
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3 Quantum mechanical formulation was developed to understand and predict the behavior of atomic sizes particles like electrons which was not possible using classical or newtonian mechanics. We will now explain briefly the features of quantum mechanical principles: Matter behaves like a particle with attributes like momentum, kinetic energy, potential energy as well as a wave with properties such as diffraction, interference and others related to the wave nature. Similarly, energy, which we understood as being electromagnetic waves, can behave like particles called photons with energy of each photon given by E = h where is the frequency of the electromagnetic wave.
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5 EE2 Fall 2007 class 2 • Another important feature of the quantum particles is that they obey the uncertainty principle . • Uncertainty Principle states that it is not possible to measure the position and momentum simultaneousl y (at the same time) with any degree of accuracy or precision that the measuring equipment is capable of providing. There is a minimum uncertainty in measurement of either of the two variables determined by the uncertainty in measurement of the other.
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6 p x x = h where p x is the uncertainty in the measurement of x- component of momentum, x is the uncertainty in the measurement of the x-component of position and h is Planck’s constant. What this means is that as the precision of measurement of momentum is increased i.e., when the uncertainty p x is decreased, the position can not be measured with any more precision than x h / p x • In this sense, the minimum uncertainty product is h. This is illustrated in the next figure.
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This note was uploaded on 01/24/2012 for the course EE 3 taught by Professor Staff during the Spring '08 term at UCLA.

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2_1_Lecture_2 - EE 2 Fall 2007 Class 2 slides 1 Class 2 Outline of lecture Brief summary of the features of quantum mechanics Particle in free

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