Author: Tru Physics
-
Problem 2.1 – Griffith’s Intro to QM
Problem 2.1 Prove the following three theorems: (a) For normalizable solutions, the separation constant must be real. Hint: Write (in Equation 2.7) as (with and real), and show that if Equation 1.20 is to hold for all , must be zero. (b) The time-independent wave function can always be taken to be real (unlike ,…
-
Chapter 5: Electric Potential Energy
5.1 Introduction to Electric Potential Energy Electric potential energy is the energy an electrically charged object possesses due to its position within an electric field. This type of energy is a scalar quantity and is an essential concept for understanding the behavior of charged particles in electric fields. 5.2 Definition of Electric Potential Energy The…
-
Chapter 4: Gauss’ Law
4.1 Introduction to Gauss’ Law Gauss’ Law is a fundamental principle in electromagnetism that relates the net electric flux through a closed surface to the total charge enclosed by that surface. This law helps simplify the calculation of electric fields in situations with symmetry and is crucial in understanding the behavior of electric fields around…
-
Chapter 3: Electric Flux
3.1 Introduction to Electric Flux Electric flux is a measure of the electric field passing through a given surface. It helps us understand how the electric field interacts with objects and how charges distribute themselves on the surfaces of objects. In this chapter, we will discuss the concept of electric flux in more detail and…
-
Chapter 2: Electric Fields
2.1 Introduction to Electric Fields Electric fields are all around us. An electric field is a region surrounding a charged object where another charged object experiences a force due to electrostatic attraction or repulsion. The electric field () is a vector quantity, meaning it has both magnitude and direction. The electric field is defined as…
-
Chapter 1: Electric Charge and Coulomb’s Law
1.1 Introduction to Electric Charge Electric charge is a fundamental property of matter. There are two types of electric charge: positive and negative. Objects with like charges repel each other, while objects with opposite charges attract each other. The fundamental unit of charge is the elementary charge which is the charge of a proton (positive)…
-
Problem 7.10 (Schroeder’s Intro to Thermal Physics)
Problem 7.10 Consider a system of five particles, inside a container where the allowed energy levels are nondegenerate and evenly spaced. For instance, the particles could be trapped in a one-dimensional harmonic oscillator potential. In this problem you will consider the allowed states for this system, depending on whether the particles are identical fermions, identical…
-
Problem 7.9 (Schroeder’s Intro to Thermal Physics)
Problem 7.9 Compute the quantum volume for an molecule at room temperature, and argue that a gas of such molecules at atmospheric pressure can be treated using Boltzmann statistics. At about what temperature would quantum statistics become relevant for this system (keeping the density constant and pretending that the gas does not liquefy)? Solution: Problem…
-
Problem 7.8 (Schroeder’s Intro to Thermal Physics)
Problem 7.8 Suppose you have a “box” in which each particle may occupy any of 10 single-particle states. For simplicity, assume that each of these states has energy zero. (a) What is the partition function of this system if the box contains only one particle? (b) What is the partition function of this system if…
-
Problem 7.6 (Schroeder’s Intro to Thermal Physics)
Problem 7.6 Show that when a system is in thermal and di⌥usive equilibrium with a reservoir, the average number of particles in the system is where the partial derivative is taken at fixed temperature and volume. Show also that the mean square number of particles is Use these results to show that the standard deviation…