Understanding how the brain works, for example, consciousness and quail, is the great challenge facing modern science. How mental world is based on the contemporary neurobiology of the brain is essentially fascinating and significant subject which has been intensively under investigation recently. Many researchers from a variety of scientific backgrounds such as physiology, neurology, physics, engineering and mathematics are being drawn to this field named neuroscience. Historically, descriptions about the brain function could go back to the ancient Egyptian era when the surgical operations to prepare mammies were conducted for the funeral ceremony of Pharaohs. The millstone of the history for searching mind was originated from the philosophical view point introduced by Ren Descartes who proposed "Cartesian dualism" in 17th century. In the present article, we cast light on the results of recent investigations concerning the brain function such as consciousness and qualia which are being carried out specially by applying Quantum Mechanics. One of the most important topics in these fascinating researches was proposed in a book entitled "Emperor's New Mind" written in 1997 by English physicist Roger Penrose. He proposed that the G del's Incompleteness Theorems and Quantal Mechanics play important roles in the consciousness by developing his idea in comparison with the strong Artificial Intelligence (strong AI). However, his unique idea still remains under discussion. Recently, several interesting studies about biological phenomenon such as photosynthesis, enzyme function etc. have been partly succeeded by applying Quantal Mechanics to their microscopic mechanisms. Especially, ion channels, which are composed of proteins and the elementary functional units for producing electrical signals (action potentials and synaptic potentials) that are basic substrates for the functions of the central nervous system, are investigated. Ionic channels inserted in the neuron membrane have several characteristic properties, for example, ion permeability, selectivity, and conductance that are usually examined experimentally by electrophysiological techniques. Furthermore, the inside of the ion channel through which ions pass from outside to inside of the neuron and vice versa has been surrounded by atoms and molecules located at the inner wall of channel proteins. Bernroider performed a quantum mechanical simulation of an ion passing through an ion channel, and discovered that the ion is delocalized when it travels through the channel: more of a coherent wave than a particle. Other possible examples of neural processes that could be treated by quantum mechanical approach are presented in this article.