We solve the time-independent Schro¨dinger equation for spher-ically symmetric potentials. First, we consider simple cases of a particle on a ring and a particle on a sphere to illustrate the degeneracy arising due to symmetry. We then consider three different spherically symmetric potentials: (i) spherical well potential, (ii) isotropic three-dimensional harmonic oscillator, and (iii) spherically confined isotropic three-dimensional har-monic oscillator. Our discussion mainly focuses on the energy levels of the bound states and the associated degeneracies. Finally, we calculate the heat capacity of endohedral fullerenes using two simple models—particle in a spherical box and con-fined harmonic oscillator.

Three modern optical telescopes of sizes 1.3-m, 3.6-m, and 4-m are installed at Devasthal, Nainital, located in the central Himalayan region of Kumaun, Uttarakhand. The 3.6-m Devasthal optical telescope is designed to be a technologically advanced and complex astronomy instrument. All three telescopes are used for night observations of celestial objects. The sky performance of the 3.6-m telescope is not only internationally competitive but also at par with the performance of other similar telescopes located elsewhere in the world. This article provides the global importance of the Devasthal observatory for optical and near-infrared observations in the present era of multi-wavelength astronomical studies.

Katydids use species-specific sound signals for courtship and long-distance communication. These sound signals are the product of intense selection pressures, both natural and sexual, while simultaneously being affected by physiological and environmental limitations. Their unique communication pat-terns and high sensitivity to ecological disturbances make them an important system to understand animal behavior, as well as ecosystem changes. This article introduces readers to acoustic communication in katydids and the significance of sound in their lives.

In this article, we will see why all the axioms of a vector space are important in its definition. During a regular course, when an undergraduate student encounters the definition of vector spaces for the first time, it is natural for the student to think of some axioms as redundant and unnecessary. In this article, we shall deal with only one axiom 1 · v = v and its importance. In the article, we would first try to prove that it is redundant just as an undergraduate student would (in the first attempt), and then point out the mistake in the proof, and provide an example which will be sufficient to show the importance of the axiom.

Here, we review some of the recent developments in quantum optics. After a brief introduction to the historical development of the subject, we discuss some of the modern aspects of quantum optics including atom field interactions, quantum state engineering, metamaterials and plasmonics, optomechanical systems, PT (parity-time) symmetry in quantum optics, as well as, quasi-probability distributions and quantum state tomography. Further, the recent developments in topological photonics is briefly discussed. The potent role of the subject in the development of our understanding of quantum physics and modern technologies is highlighted.

Luminescent coating, more popularly known as pressure-sensitive paint (PSP) is a relatively new aerodynamic measurement tool for providing a field measurement of pressure over a model surface in wind tunnel testing. It provides information on the flow anomalies present at any point on the surface, unlike the discrete data from pressure taps. The technique is based on the principle of dynamic luminescence quenching of luminescent molecules present in the paint by oxygen molecules. PSP coating comprises luminescent sensor molecules embedded in an oxygen-permeable binder. On illumination with light of an appropriate wavelength, the coat-ing exhibits luminescence. The luminescence of the PSP coat-ing is inversely related to the surface pressure on the coated model. This article discusses these aspects in detail and provides an overview of the work carried out in this direction across the world.

Since all of us have been children at some time in our lives, and many of us have also been parents at other times, we are well aware of the psychological and physiological importance of parental care, both for the offspring as well as for the parents. But at the same time, we are also painfully aware that there is often some conflict between parents and their offspring about the amount of parental investment that should flow from parents to offspring. As evolutionary biologists, however, we must pause and ask: why the conflict? According to the theory of natural selection, living organisms are expected to maximize their Darwinian fitness. Since offspring are the currency of Darwinian fitness, should not ‘parent-offspring conflict’ be an oxymoron? Why should there be a conflict between parents and offspring? Offspring should be selected to survive and grow, and have offspring of their own, and parents should be selected to do everything in their power to help the offspring to achieve their goals. Indeed, there is no parent-offspring conflict in some species, notably, in those species that produce a single offspring or produce all their offspring in one go, and die. There is nothing more important for parents of such species than the welfare of their offspring, leaving no scope for parent-offspring conflict.