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Expectation Values of Position & Momentum | Basics of Probability Theory | OPERATORS
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What are Operators in Quantum mechanics? What is the Expectation value of Position, Momentum, Kinetic Energy, Total Energy etc? This is what we discuss in today's lecture.
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𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬
In quantum mechanics, expectation values and operators are essential concepts for describing particle behavior. The position operator (X) and momentum operator (P) represent measurable quantities. The expectation value of position, ⟨x⟩, is the average position calculated from the probability density function |ψ(x)|^2. Similarly, the expectation value of momentum, ⟨p⟩, is computed using the probability density function and the momentum operator, often expressed as -iħ(d/dx). These operators and their expectation values provide a probabilistic framework for understanding the behavior of particles, with the uncertainty principle highlighting the inherent limitations in simultaneously measuring position and momentum precisely.
In this video I describe basics of probability theory, derive the expectation values of position, momentum, kinetic energy and total energy. I also discuss the operators corresponding to these quantities.
00:00 Introduction
04:15 Basics of Probability Theory
14:35 Expectation Value of Position
26:58 Expectation Value of Momentum
42:52 Expectation Values & Operators
48:38 Kinetic Energy Operator
51:29 Total Energy Operator
𓏬𓏬𓏬𓏬𓏬𓏬TELEGRAM𓏬𓏬𓏬𓏬𓏬𓏬
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Your Financial support provides me an additional incentive to create high quality lecture videos. I am very much thankful for your generosity and kindness
JOIN MEMBERSHIP in Youtube 😇😇😇
𓏬𓏬𓏬𓏬𓏬ELEVATE CLASSES𓏬𓏬𓏬𓏬𓏬
𓏬𓏬𓏬𓏬𓏬LEC NOTES - GDRIVE𓏬𓏬𓏬𓏬𓏬
𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬
In quantum mechanics, expectation values and operators are essential concepts for describing particle behavior. The position operator (X) and momentum operator (P) represent measurable quantities. The expectation value of position, ⟨x⟩, is the average position calculated from the probability density function |ψ(x)|^2. Similarly, the expectation value of momentum, ⟨p⟩, is computed using the probability density function and the momentum operator, often expressed as -iħ(d/dx). These operators and their expectation values provide a probabilistic framework for understanding the behavior of particles, with the uncertainty principle highlighting the inherent limitations in simultaneously measuring position and momentum precisely.
In this video I describe basics of probability theory, derive the expectation values of position, momentum, kinetic energy and total energy. I also discuss the operators corresponding to these quantities.
00:00 Introduction
04:15 Basics of Probability Theory
14:35 Expectation Value of Position
26:58 Expectation Value of Momentum
42:52 Expectation Values & Operators
48:38 Kinetic Energy Operator
51:29 Total Energy Operator
𓏬𓏬𓏬𓏬𓏬𓏬TELEGRAM𓏬𓏬𓏬𓏬𓏬𓏬
𓏬𓏬𓏬𓏬𓏬SUPPORT CHANNEL𓏬𓏬𓏬𓏬𓏬
Your Financial support provides me an additional incentive to create high quality lecture videos. I am very much thankful for your generosity and kindness
JOIN MEMBERSHIP in Youtube 😇😇😇
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