Lecture

Semiclassical Propagator: Explicit Formulation

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In course

PHYS-426: Quantum physics IV

Introduction to the path integral formulation of quantum mechanics. Derivation of the perturbation expansion of Green's functions in terms of Feynman diagrams. Several applications will be presented, including non-perturbative effects, such as tunneling an ...

Description

This lecture delves into the semiclassical propagator, starting with a review of the previous lecture's content. The focus is on obtaining a more explicit formula for the function psi zero of tf, connecting it to the classical velocity and action. By deriving the relationship between the classical action and the function psi zero, the instructor demonstrates how the semiclassical propagator can be expressed in terms of the second derivative of the action. This leads to the Van Vleck - Pauli - Morette formula, a key result in quantum physics. The lecture concludes by hinting at a shift to a new topic, the fixed energy propagator.

Instructors (2)

Giuseppe Carleo

Giuseppe Carleo is a computational quantum physicist, whose main focus is the development of advanced numerical algorithms tostudy challenging problems involving strongly interacting quantum systems.He is best known for the introduction of machine learning techniques to study both equilibrium and dynamical properties,based on a neural-network representations of quantum states, as well for the time-dependent variational Monte Carlo method.He earned a Ph.D. in Condensed Matter Theory from the International School for Advanced Studies (SISSA) in Italy in 2011.He held postdoctoral positions at the Institut d’Optique in France and ETH Zurich in Switzerland, where he alsoserved as a lecturer in computational quantum physics.In 2018, he joined the Flatiron Institute in New York City in 2018 at the Center for Computational Quantum Physics (CCQ), working as a Research Scientist and project leader, and also leading the development of the open-source project NetKet.Since September 2020 he is an assistant professor at EPFL, in Switzerland, leading the Computational Quantum Science Laboratory (CQSL).

Riccardo Rossi

Official source

Related concepts (22)

Path integral formulation

The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization.

Measurement in quantum mechanics

In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule.

Philosophy of physics

In philosophy, philosophy of physics deals with conceptual and interpretational issues in modern physics, many of which overlap with research done by certain kinds of theoretical physicists. Philosophy of physics can be broadly divided into three areas: interpretations of quantum mechanics: mainly concerning issues with how to formulate an adequate response to the measurement problem and understand what the theory says about reality.

Quantum indeterminacy

Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. Prior to quantum physics, it was thought that Quantum indeterminacy can be quantitatively characterized by a probability distribution on the set of outcomes of measurements of an observable. The distribution is uniquely determined by the system state, and moreover quantum mechanics provides a recipe for calculating this probability distribution.

Quantum information science

Quantum information science is a field that combines the principles of quantum mechanics with information science to study the processing, analysis, and transmission of information. It covers both theoretical and experimental aspects of quantum physics, including the limits of what can be achieved with quantum information. The term quantum information theory is sometimes used, but it does not include experimental research and can be confused with a subfield of quantum information science that deals with the processing of quantum information.

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