Answered: Discuss why we use integration in…

Discuss why we use integration in physics ? Andalso Find the Integration of the FOLLOWING function w.r.tu f(u) = tan u2 + cos 2u

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 39P

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A one-dimensional infinite potential well has a length of 2L. i) What are the energy eigenvalues? ii) Calculate the ground state energy if ten protons are confined in the box. Assume that the protons don’t interact with each other.
A pesky 1.5 mg mosquito is annoying you as you attempt to study physics in your room, which is 5.0 m wide and 2.5 m high. You decide to swat the bothersome insect as it flies toward you, but you need to estimate its speed to make a successful hit. (a) What is the maximum uncertainty in the horizontal position of the mosquito? (b) What limit does the Heisenberg uncertainty principle place on your ability to know the horizontal velocity of this mosquito? Is this limitation a serious impediment to your attempt to swat it?
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A particle in an infinite well is in the ground state with energy1.54eV. How much energy must be added to the particle to reach the second excited state (n = 3)? The third excited state (n = 4)?
Check your Understanding (a) Consider an infinite square well with wall boundaries x=0 and x=L. What is the of finding a quantum panicle in its state somewhere between x=0 and x=L/4? (b) Repeat question (a) for a classical panicle.
Suppose that an electron trapped in a one-dimensional infinite well of width 250 pm is excited from its first excited state to its third excited state. (a) What energy must be transferred to the electron for this quantum jump? The electron then de-excites back to its ground state by emitting light. In the various possible ways it can do this, what are the (b) shortest, (c) second shortest, (d) longest, and (e) second longest wavelengths that can be emitted? (f) Show the various possible ways on an energy-level diagram. If light of wavelength 29.4 nm happens to be emitted, what are the (g) longest and (h) shortest wavelength that can be emitted afterwards?
The spherical harmonics are the eigenfunctions of ?̂2 and ?̂ ? for the rigid rotor and thehydrogen atom (and other spherically symmetric problems). In this problem, we willexamine the nature of the angular nodes for these systems.Since the spherical harmonics include a factor of eim, which never has magnitude zero, forthis exercise we will construct some linear combinations of the spherical harmonics so weare working with real-valued functions. Two of the real-valued spherical harmonics are:12 (?1−1 + ?11) = 12 √ 32? sin ? cos ? 12? (?32 − ?3−2) = 14 √1052? sin2 ? cos ? sin 2?(a) Determine the angles at which nodal surfaces will occur for each of these functions, anddescribe the nature of the nodal surfaces that they represent. In other words, identifythe locations of nodal planes and other surfaces in the Cartesian axis system.(b) What atomic orbitals (e.g. 1s, 2p, etc.) are represented by these functions and what isthe total number of distinct angular nodal surfaces?
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Q 3: Two people measure a wave of a particle passing from a point in front of them and their measurements are as follows: First person: W, (x,t) = Acos(5x — 3t) Second person: W,(x,t) = Acos(5.1x — 3.2t) 1 Find the wave packet consisting of these two waves in its simplest form. 2 2-If you know that at time t = 0.1s in position x = 1m, The wave packet was ¥(x.t) = 7.9726375772 what is the value of the constant A