Author: Tru Physics
-
Hall Effect
The Hall effect is a phenomenon in which a voltage is generated across a conductor when an electric current flows through it and a magnetic field is applied perpendicular to the direction of the current. This effect was discovered by Edwin Hall in 1879 and has since been widely used in various applications, including measuring…
-
Chapter 7: Capacitors
7.1 Introduction to Capacitors Capacitors are passive electrical components that store electrical energy in an electric field. They consist of two conductive plates separated by an insulator (dielectric) material. Capacitors are widely used in electronic circuits for various purposes, such as energy storage, filtering, and coupling or decoupling of signals. 7.2 Capacitance Capacitance is defined…
-
Chapter 6: The Gradient Operator
6.1 Introduction to the Gradient Operator The gradient operator () is a vector differential operator that helps understand how a scalar field changes in space. In the context of electric potential, the gradient operator allows us to find the electric field given the electric potential. 6.2 The Gradient Operator Defined The gradient operator is defined…
-
Problem 2.8 – Griffith’s Intro to QM
Problem 2.8 A particle of mass m in the infinite square well (of width starts outin the state for some constant , so it is (at ) equally likely to be found at any point in the left half of the well. What is the probability that a measurement of the energy (at some later…
-
Problem 2.7 – Griffith’s Intro to QM
Problem 2.7 A particle in the infinite square well has the initial wave function (a) Sketch , and determine the constant (b) Find .(c) What is the probability that a measurement of the energy would yield the value ?(d) Find the expectation value of the energy, using Equation 2.2. Solution: Peoblem 2.7 Solution (Download)
-
Problem 2.6 – Griffith’s Intro to QM
Problem 2.6 Although the overall phase constant of the wave function is of no physical significance (it cancels out whenever you calculate a measurable quantity), the relative phase of the coefficients in Equation 2.17 does matter. For example, suppose we change the relative phase of and in Problem 2.5: where is some constant. Find ,…
-
Problem 2.5 – Griffith’s Intro to QM
Problem 2.5 A particle in the infinite square well has as its initial wave function an even mixture of the first two stationary states: (a) Normalize . (That is, find This is very easy, if you exploit the orthonormality of and . Recall that, having normalized at , you can rest assured that it stays…
-
Problem 2.4 – Griffith’s Intro to QM
Problem 2.4 Calculate , , , , , and , for the nth stationary state of the infinite square well. Check that the uncertainty principle is satisfied. Which state comes closest to the uncertainty limit? Solution: Problem 2.4 Solution (Download)
-
Problem 2.3 – Griffith’s Intro to QM
Problem 2.3 Show that there is no acceptable solution to the (time-independent) Schrödinger equation for the infinite square well with or . (This is a special case of the general theorem in Problem 2.2, but this time do it by explicitly solving the Schrödinger equation, and showing that you cannot satisfy the boundary conditions.) Solution:…
-
Problem 2.2 – Griffith’s Intro to QM
Problem 2.2 Show that must exceed the minimum value of , for every normalizable solution to the time-independent Schrödinger equation. What is the classical analog to this statement? Hint: Rewrite Equation 2.5 in the form if , then and its second derivative always have the same sign—argue that such a function cannot be normalized. Solution:…