Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

Miscellanea in Elementary Quantum Mechanics, I

K. Husimi

Published Mar 1, 1953• 43 citations
Publisher

Abstract

In the course of lectures on quantum mechanics delivered for the undergraduate students of this university I have encountered a number of examples of more or less novelty and interest, which I want here in a series of papers to present before a wider circle. Since the familiarity with all kinds of problems leads eventually to a better understanding of quantum mechanics, just as we have been possessed with the complete master of classical mechanics only through the numerous exercises in schools, it would, I hope, be of some service for a future development of quantum theory. Some of matters I present are of older date and some of recent date.

DOI
10.1143/ptp.9.238

Related papers

Lectures on Quantum Mechanics

Gordon Baym

These lecture notes comprise a three-semester graduate course in quantum mechanics at the University of Illinois. There are a number of texts which present the basic topics very well; but since a fair quantity of the material discussed in my course was not available to the students in elementary quantum mechanics books, I was asked to prepare written notes. In retrospect these lecture notes seemed sufficiently interesting to warrant their publication in this format. The notes, presented here in slightly revised form, consitutute a self-contained course in quantum mechanics from first principles to elementary and relativistic one-particle mechanics. Prerequisite to reading these notes is some familiarity with elementary quantum mechanics, at least at the undergraduate level. Preferably the reader should already have met the uncertainty principle and the concept of a wave function. Prerequisites also include sufficient acquaintance with complex cariables to be able to do simple contour integrals and to understand words such as "poles" and "branch cuts." An elementary knowledge of Fourier transforms and series is necessary. I also assume an awareness of classical electrodynamics.

CRC Press eBooks•Mar 5, 2018•575 citations

On some experiments leading to a revision of the foundations of quantum mechanics

A.B. Datzeff

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B•Sep 1, 1975•6 citations

Lectures on Quantum Mechanics for Mathematics Students

L. D. Faddeev, O. Yakubovskiĭ

This book is based on notes from the course developed and taught for more than 30 years at the Department of Mathematics of Leningrad University. The goal of the course was to present the basics of quantum mechanics and its mathematical content to students in mathematics. This book differs from the majority of other textbooks on the subject in that much more attention is paid to general principles of quantum mechanics. In particular, the authors describe in detail the relation between classical and quantum mechanics. When selecting particular topics, the authors emphasize those that are related to interesting mathematical theories. In particular, the book contains a discussion of problems related to group representation theory and to scattering theory. This book is rather elementary and concise, and it does not require prerequisites beyond the standard undergraduate mathematical curriculum. It is aimed at giving a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.

Student mathematical library•Mar 9, 2009•54 citations

Dense Summary of New Developments in Quantum Mechanics

Espen Gaarder Haug

In this note, we present a table with a summary of recent developments in quantum mechanics. If you not have studied our papers carefully already [1–4], then this paper will not make much sense and the equations could easily be misunderstood, so we strongly encourage the reader to become familiar with this material first. We will possibly write a long paper on this topic later, but it may be helpful to present the essence of both old and new QM, as we understand it today. This is useful for both tracing the history of ideas related to QM in mathematical form and for creating an opportunity to compare equations and analyze their similarities and differences.

•Jan 1, 2020•0 citations

Miscellaneous Results from Elementary Quantum Mechanics

Hans Albrecht Bethe

This chapter will serve to summarize the results of elementary quantum mechanics and to set the notation that will be employed in this book. For a more complete treatment of these topics, the reader is referred to any textbook on quantum mechanics.

CRC Press eBooks•Nov 23, 2018•1 citation

Lectures On Spin Dynamics: The Theoretical Minimum

Giuseppe Pileio

This book consists of a series of lectures introducing what the author believes to be the theoretical minimum for the understanding of nuclear spin dynamics, the branch of physics underpinning magnetic resonance techniques such as NMR and MRI. Spin dynamics ultimately concern the study of the state and time evolution of systems made by a large collection of particles possessing spin, one of the most subtle and indeed fascinating concepts in relativistic quantum mechanics and whose understanding requires a mix of quantum mechanics, Hamiltonian dynamics and advanced mathematics. Written in the concise and direct style appropriate for university lectures, this book is addressed to both undergraduate and postgraduate students who are approaching magnetic resonance studies and want to reach the theoretical minimum required to understand the wider topic and its main applications. The book is suitable for researchers who work in the field of magnetic resonance and want to know more about its theoretical fundamentals. Finally, built as a complete set of 12 lectures and 4 workshops, the book can act as a solid reference to lecturers of magnetic resonance university modules. Trained in a world-leading research laboratory internationally recognised for its contributions to the NMR field, the author has a track record in theoretical and methodological developments of nuclear spin dynamics. In this book, he tries to merge his passion for the understanding of physics through its mathematical rendering with his personal quest for the elegance of a clean, clear and satisfactory explanation.

Royal Society of Chemistry eBooks•Jun 13, 2022•1 citation
In the course of lectures on quantum mechanics delivered for the undergraduate students of this university I have encountered a number of examples of more or less novelty and interest, which I want here in a series of papers to present before a wider circle. Since the familiarity with all kinds of problems leads eventually to a better understanding of quantum mechanics, just as we have been possessed with the complete master of classical mechanics only through the numerous exercises in schools, it would, I hope, be of some service for a future development of quantum theory. Some of matters I present are of older date and some of recent date.
These lecture notes comprise a three-semester graduate course in quantum mechanics at the University of Illinois. There are a number of texts which present the basic topics very well; but since a fair quantity of the material discussed in my course was not available to the students in elementary quantum mechanics books, I was asked to prepare written notes. In retrospect these lecture notes seemed sufficiently interesting to warrant their publication in this format. The notes, presented here in slightly revised form, consitutute a self-contained course in quantum mechanics from first principles to elementary and relativistic one-particle mechanics. Prerequisite to reading these notes is some familiarity with elementary quantum mechanics, at least at the undergraduate level. Preferably the reader should already have met the uncertainty principle and the concept of a wave function. Prerequisites also include sufficient acquaintance with complex cariables to be able to do simple contour integrals and to understand words such as "poles" and "branch cuts." An elementary knowledge of Fourier transforms and series is necessary. I also assume an awareness of classical electrodynamics.
This book is based on notes from the course developed and taught for more than 30 years at the Department of Mathematics of Leningrad University. The goal of the course was to present the basics of quantum mechanics and its mathematical content to students in mathematics. This book differs from the majority of other textbooks on the subject in that much more attention is paid to general principles of quantum mechanics. In particular, the authors describe in detail the relation between classical and quantum mechanics. When selecting particular topics, the authors emphasize those that are related to interesting mathematical theories. In particular, the book contains a discussion of problems related to group representation theory and to scattering theory. This book is rather elementary and concise, and it does not require prerequisites beyond the standard undergraduate mathematical curriculum. It is aimed at giving a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.
In this note, we present a table with a summary of recent developments in quantum mechanics. If you not have studied our papers carefully already [1–4], then this paper will not make much sense and the equations could easily be misunderstood, so we strongly encourage the reader to become familiar with this material first. We will possibly write a long paper on this topic later, but it may be helpful to present the essence of both old and new QM, as we understand it today. This is useful for both tracing the history of ideas related to QM in mathematical form and for creating an opportunity to compare equations and analyze their similarities and differences.
This book consists of a series of lectures introducing what the author believes to be the theoretical minimum for the understanding of nuclear spin dynamics, the branch of physics underpinning magnetic resonance techniques such as NMR and MRI. Spin dynamics ultimately concern the study of the state and time evolution of systems made by a large collection of particles possessing spin, one of the most subtle and indeed fascinating concepts in relativistic quantum mechanics and whose understanding requires a mix of quantum mechanics, Hamiltonian dynamics and advanced mathematics. Written in the concise and direct style appropriate for university lectures, this book is addressed to both undergraduate and postgraduate students who are approaching magnetic resonance studies and want to reach the theoretical minimum required to understand the wider topic and its main applications. The book is suitable for researchers who work in the field of magnetic resonance and want to know more about its theoretical fundamentals. Finally, built as a complete set of 12 lectures and 4 workshops, the book can act as a solid reference to lecturers of magnetic resonance university modules. Trained in a world-leading research laboratory internationally recognised for its contributions to the NMR field, the author has a track record in theoretical and methodological developments of nuclear spin dynamics. In this book, he tries to merge his passion for the understanding of physics through its mathematical rendering with his personal quest for the elegance of a clean, clear and satisfactory explanation.