Tru Physics

Author: Tru Physics

  • Problem 3.3 – Griffith’s Intro to QM

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    Problem 3.3 Show that if for all h (in Hilbert space), then for all f and g (i.e. the two definitions of “hermitian”—Equations 3.16 and 3.17—are equivalent). Hint: First let , and then let . Solution: Problem 3.3 Solution (Download)

  • Problem 3.2 – Griffith’s Intro to QM

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    Problem 3.2 (a) For what range of is the function in Hilbert space, on the interval ? Assume is real, but not necessarily positive.(b) For the specific case , is in this Hilbert space? What about ? How about ? Solution: Problem 3.2 Solution (Download)

  • Problem 3.1 – Griffith’s Intro to QM

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    Problem 3.1 (a) Show that the set of all square-integrable functions is a vector space (refer to Section A.1 for the definition). Hint: The main point is to show that the sum of two square-integrable functions is itself square-integrable. Use Equation 3.7. Is the set of all normalized functions a vector space?(b) Show that the…

  • Five Percent Interval Calculator

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    Occasionally, it is necessary to generate a five percent interval around a certain value. That’s why we have added this five percent interval calculator. Though a very simple calculator, sometimes it’s nice to speed up this tedious calculation, especially when creating online quizzes and other course materials.

  • Chapter 9: Newton’s Laws of Motion

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    9.1 Introduction to Newton’s Laws of Motion Newton’s Laws of Motion are the fundamental laws of Physics I. He originally wrote these laws in Philosophiae Naturalis Principia Mathematica, more commonly known today as the Principia. The three laws can be stated in words as: or mathematically as: 9.2 Newton’s First Law The First Law is…

  • Chapter 8: Force Diagrams (Free-Body Diagrams)

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    8.1 Introduction to Force Diagrams Force diagrams, also known as free-body diagrams, are visual representations that show the forces acting on an object. These diagrams are an essential tool in understanding and analyzing the behavior of objects under the influence of various forces. Drawing a force diagram is often step one in solving for the…

  • Chapter 7: Forces

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    7.1 Introduction to Forces: Push and Pull Forces are an essential concept in physics. A force can cause an object to move, stop, speed up, slow down, or change direction. They do this via a “push” or “pull” action. Forces are typically measured in Newtons There are different methods of categorizing forces. One way is…

  • Chapter 3: Vector Components

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    3.1 Introduction It is often necessary to break a vector into its components. In the cartesian coordinate system, this would mean breaking the vector into an x-component and a y-component. Figure 1 below demonstrates that there are generally two ways to do this as represented by the two different right triangles. It is important to…

  • Newton’s Third Law

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    Forces come in pairs which are of the same magnitude but opposite direction. Newton’s third law of motion, also known as the law of action and reaction, is one of the fundamental principles of classical mechanics. One of the statements of the third law is that forces come in pairs. This means that if object…

  • Newton’s Second Law

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    The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Newton’s Second Law of Motion is one of the fundamental principles of physics. It states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional…