Snippets of physics

How does one study quantum mechanics in an accelerated frame? The answer to this question leads to some surprising insights into the solutions of the Schräodinger equation for harmonic oscillator!     

Snippets of physics

The idealized flow of fluid around a spherical body is a classic textbook problem in fluid mechanics. Interestingly enough, it leads to some curious twists and turns and conceptual conundrums. T Padmanabhan works at IUCAA, Pune and is interested in all areas of theoretical physics, especially those which have something to do with gravity.     

Snippets of physics

One of the celebrated results in black hole physics is that black holes have a temperature and they emit a thermal spectrum of radiation. Though a rigorous derivation of this result requires quantum field theory, a flavour of the essential ideas can be provided at an elementary level as indicated here. T Padmanabhan works at IUCAA, Pune and is interested in all areas of theoretical physics, especially those which have something to do with gravity. This is based on an article originally published by the author in Physics Education, Vol. 24, p.67, 2007.     

Snippets of physics

The gravitational field of a massive, spherical, body like the Sun is described in general relativity by a solution to Einstein’s equations called the Schwarzschild soution. Here is an elementary persepective on this solution, which — though far from a rigourous derivation — raises intriguing questions. T Padmanabhan works at IUCAA, Pune and is interested in all areas of theoretical physics, especially those which have something to do with gravity. This is based on an article originally published by the author in Physics Education, Vol. 23, No.1, p.47, 2006.     

Snippets of physics

The probability amplitude for a particle to propagate from event to event in spacetime shows some nice similarities with the corresponding propagator for the electromagnetic wave amplitude discussed in the last installment. In fact, this analogy provides an interesting insight into the transition from quantum field theory to quantum mechanics! T Padmanabhan works at IUCAA, Pune and is interested in all areas of theoretical physics, especially those which have something to do with gravity.     

Snippets of physics

Few processes in nature are as ubiquitous as the random walk which combines extraordinary simplicity of concept with considerable complexity in the final output. In this and the next installment, we shall examine several features of this remarkable phenomenon.     

Snippets of physics

It is well known in Newtonian gravity that a spherically symmetric density distribution produces a force outside it which falls as the square of the distance. Surprisingly, the converse is not true! Just be cause the force falls as inverse square outside a density distribution, you cannot conclude that it must be spherically symmetric. This article, first in a new series, explores this and related issues. This is based on an article originally published by the author in Physics Education, Vol 22, No. 4, p.263, 2006. T Padmanabhan works at IUCAA, Pune and is interested in all areas of theoretical physics, especially those which have something to do with gravity.     

Snippets of physics

Discovering unexpected connections between completely different phenomen a is always a delight in physics. In this and the next installment, we will look at one such connection between two unlikely phenomena: propagation of light and path integral approach to quantum mechanics! T Padmanabhan works at IUCAA, Pune and is interested in all areas of theoretical physics, especially those which have something to do with gravity.     

Snippets of physics

Scaling arguments and dimensional analysis are powerful tools in physics which help you to solve several interesting problems. And when the scaling arguments fail, as in the examples discussed here, we are led to a more fascinating situation. T Padmanabhan works at IUCAA, Pune and is interested in all areas of theoretical physics, especially those which have something to do with gravity.     

Snippets of physics

The statistical mechanics of a system of particles interacting through gravity leads to several counter-intuitive features. We explore one of them, called Antonov instability, in this installment.     

Snippets of physics

The major contribution of Kepler was in discovering his laws of planetary motion, one of which states that planets move in elliptical orbits around the Sun which is located at one of the foci of the ellipse. The motion of a test particle in an inverse square force law is usually called the Kepler problem. We will examine several aspects of this motion in this last installment of Snippets in Physics.     

Snippets of physics

Some of the curious effects in quantum theory and statistical mechanics can be interpreted by analytically continuing the time coordinate to purely inaginary values. We explore some of these issues in this instalment.     

Snippets of physics

Many features of the expanding universe, which should be legitimately discussed using general relativity, can be sneaked in by using Newtonian physics in an expanding coordingate system. In this special issue on Hubble, I describe several of these features along with some cautionary comments.     

Snippets of physics

A solution to the 3-body problem in gravity, due to Lagrange, has several remarkable features. In particular, it describes a situation in which a particle, located at the maxima of a potential, can remain stable against small perturbations.     

Snippets of physics

The Foucault pendulum is an elegant device that demonstrates the rotation of the Earth. After describing it, we will elaborate on an interesting geometrical relationship between the dynamics of the Foucault pendulum and Thomas precession discussed in the last installment¹. This will help us to understand both phenomena better. T Padmanabhan works at IUCAA, Pune and is interested in all areas of theoretical physics, especially those which have something to do with gravity.     

Snippets of physics

Thomas precession is a curious effect in special relativity which is purely kinematical in origin and illustrates some important features of the Lorentz transformation. It also has a beautiful geometric interpretation. We will explore these in this and the next installment. T Padmanabhan works at IUCAA, Pune and is interested in all areas of theoretical physics, especially those which have something to do with gravity.     

一维谐振子能量本征值两种解法探讨

介绍了波动力学中解微分方程法和代数法在求解量子力学中一维谐振子能量本征值问题中的应用,并分析讨论了这两种方法的特点。     

一维谐振子系综密度矩阵的计算

在能量表象和坐标表象中,分别计算了一维谐振子综的密度矩阵,并得到了在温度T时的平均密度分布,最后讨论了高温极限(T→∞)和低温极限（T→∞)．     

一维谐振子能量本征值在各种表象中的求解

给出了计算一维谐振子能量本征值的方法,它们分别是在坐标表象中求解;在动量表象中求解;在能量表象中求解和直接矢量求解。