Tag: Schrödinger Equation
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Time-Dependent Schrödinger Equation
Introduction The Time-dependent Schrödinger equation (TDSE) is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes with time. It is named after Erwin Schrödinger, who formulated the equation in 1926. The Time-dependent Schrödinger Equation The TDSE is given by: Here, is the wavefunction of the system at…
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Chapter 21: Three Dimensional Quantum Mechanics
21.1 Introduction to Three Dimensional Quantum Mechanics While we have primarily discussed one-dimensional quantum mechanics up to this point, real-world quantum systems often exist in three dimensions. The principles of quantum mechanics can be extended to describe the behavior of particles in three-dimensional space, leading to a richer understanding of physical systems and enabling the…
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Chapter 18: Particle in a Box
18.1 Introduction to Particle in a Box The particle in a box is a simplified model in quantum mechanics that helps to understand the behavior of a quantum particle confined in a one-dimensional, infinitely deep potential well. This model is important because it provides an elementary example of bound states, quantization of energy levels, and…
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Chapter 17: Introduction to Quantum Mechanics
17.1 Quantum Mechanics Overview Quantum mechanics is the branch of physics that deals with the behavior of particles at the atomic and subatomic levels. It emerged in the early 20th century as a response to the limitations of classical mechanics and electromagnetism, which failed to describe the observed behavior of particles at the microscopic scale.…
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Quantum Mechanics
Introduction Quantum Mechanics is the branch of physics that describes the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles. It is one of the fundamental theories of physics, alongside General Relativity, and has been remarkably successful in predicting experimental results. Wave-Particle Duality One of the cornerstone concepts in…
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Schrödinger Equation
The Schrödinger equation is a foundational equation in quantum mechanics that describes the evolution of quantum states over time. It was formulated by Erwin Schrödinger in 1926 and provides a mathematical framework for understanding the wave-like behavior of particles at the quantum level. The equation plays a crucial role in determining the behavior and properties…