Unit 5 Engineering Physics Notes PDF

UNIT-5 Unit 5 Quantum Mechanics A Inadequacy of classical Physics, Wave particle CO5 duality, de-Broglie wavelength B Davisson-Germer experiment, Schrodinger wave CO5, equation, CO6 C particle...

UNIT-5 Unit 5 Quantum Mechanics A Inadequacy of classical Physics, Wave particle CO5 duality, de-Broglie wavelength B Davisson-Germer experiment, Schrodinger wave CO5, equation, CO6 C particle in a 1-dimensional box, harmonic CO5, oscillator problem, CO6 Black Body: A black body is a theoretical object that absorbs 100% of the radiation that hits it. Therefore it reflects no radiation and appears perfectly black. Observations:  Experimental Results The Rayleigh–Jeans law fails to correctly reproduce experimental results. In the limit of short wavelengths, the Rayleigh–Jeans law predicts infinite radiation intensity, which is The Wien law does accurately describe the inconsistent with the experimental results in which radiation short wavelength (high-frequency) spectrum of intensity has finite values in the ultraviolet region of the thermal emission from objects, but it fails to spectrum. This divergence between the results of classical accurately fit the experimental data for long- theory and experiments, which came to be called the ultraviolet wavelength (low-frequency) emission catastrophe, shows how classical physics fails to explain the mechanism of blackbody radiation..  Introduction to Wave Particle Duality One can understand wave particle duality via the behavior of light. Diffraction and interference of light explain that it behaves as a wave. The photoelectric influence explains that it consists of particles. The phenomenon is Wave particle duality. It is also quite relevant for objects as well. The electron to football everything is assumed that it exhibits Wave-particle duality. The nature of the particle dominates in the case of large objects while wave and particle nature are shown by smaller objects. The electron shows the same interference pattern similar to light when they are passed through the double slit.  Schrödinger Equation The Schrödinger equation is indeed a cornerstone of quantum mechanics, much like Newton’s laws are for classical mechanics. Developed by Erwin Schrödinger in 1926, this equation describes how the quantum state of a physical system changes over time. It is essential for understanding the behavior of particles at the subatomic level. Schrodinger's equation describes the wave function of a quantum mechanical system, which gives probabilistic information about the location of a particle and other observable quantities such as its momentum. The most important thing you’ll realize about quantum mechanics after learning about the equation is that the laws in the quantum realm are very different from those of classical mechanics.  The Wave Function The wave function is one of the most important concepts in quantum mechanics, because every particle is represented by a wave function. It is typically given the Greek letter psi (​Ψ​), and it depends on position and time. When you have an expression for the wave function of a particle, it tells you everything that can be known about the physical system, and different values for observable quantities can be obtained by applying an operator to it.  Particle in a Box (Infinite Square Well) One of the simplest solutions to the time-independent Schrodinger equation is for a particle in an infinitely deep square well (i.e. an infinite potential well), or a one-dimensional box of base length ’a’. Of course, these are theoretical idealizations, but it gives a basic idea of how you solve the Schrodinger equation without accounting for many of the complications that exist in nature. With the potential energy set to 0 outside the well where probability density is also 0, the Schrodinger equation for this situation becomes: