In the 17th century, it was thought that motion of macroscopic and microscopic objects could be well-expressed by using the laws of classical mechanics. But towards the end of 19th century, experimental studies showed that classical mechanics failed when applied to microscopic objects. This was mainly because classical mechanics did not take into account the concept of de-Broglie’s dual nature of matter and Heisenberg’s uncertainty principle. Also, classical mechanics does not put any restrictions on the values of dynamical properties (likes position, momentum, energy etc.) calculated for microscopic object. According to classical mechanics, microscopic objects can have any value of dynamical properties, ( exact , large or small is permissible). Also any number of properties can be calculated simultaneously for a system.
In the 17th century, it was thought that motion of macroscopic and microscopic objects could be well-expressed by using the laws of classical mechanics. But towards the end of 19th century, experimental studies showed that classical mechanics failed when applied to microscopic objects. This was mainly because classical mechanics did not take into account the concept of de-Broglie’s dual nature of matter and Heisenberg’s uncertainty principle. Also, classical mechanics does not put any restrictions on the values of dynamical properties (likes position, momentum, energy etc.) calculated for microscopic object. According to classical mechanics, microscopic objects can have any value of dynamical properties, ( exact , large or small is permissible). Also any number of properties can be calculated simultaneously for a system.
In the 17th century, it was thought that motion of macroscopic and microscopic objects could be well-expressed by using the laws of classical mechanics. But towards the end of 19th century, experimental studies showed that classical mechanics failed when applied to microscopic objects. This was mainly because classical mechanics did not take into account the concept of de-Broglie’s dual nature of matter and Heisenberg’s uncertainty principle. Also, classical mechanics does not put any restrictions on the values of dynamical properties (likes position, momentum, energy etc.) calculated for microscopic object. According to classical mechanics, microscopic objects can have any value of dynamical properties, ( exact, large or small is permissible). Also any number of properties can be calculated simultaneously for a system.
Capsule history of quantum mechanics Starting in the seventeenth century, and continuing to the present day, physicists developed a body of ideas that describe much about the world around us: the motion of a cannonball, the orbit of a planet, the working of an engine, the crack of a baseball bat. This body of ideas is called classical mechanics . In 1905, Albert Einstein realized that these ideas didn't apply to objects moving at high speeds (that is, at speeds near the speed of light) and he developed an alternative body of ideas called relativistic mechanics . Classical mechanics is wrong in principle, but it is a good approximation to relativistic mechanics when applied to objects moving at low speeds. At about the same time, several experiments led physicists to realize that the classical ideas also didn't apply to very small objects, such as atoms. Over the period 1900–1927 a number of physicists (Planck, Bohr, Einstein, Heisenberg, de Broglie, Schrödinger, and others) developed an alternative quantum mechanics . Classical mechanics is wrong in principle, but it is a good approximation to quantum mechanics when applied to large objects. What is the nature of quantum mechanics? I'm not going to spend any time on the history of quantum mechanics, which is convoluted and fascinating. Instead, I will focus on the ideas developed at the end. What sort of ideas required twenty-eight years of development from this stellar group of scientists? Einstein's theory of relativity is often (and correctly) described as strange and counterintuitive.
The results of Bohr model can be used to explain the motion of macroscopic objects or big objects (like orbiting planets and sun, falling stone etc.). These macroscopic objects have essentially a particle nature and Newtonian laws of motion can be applied on them. But it fails when applied to explain the motion of microscopic objects or small objects (like electrons, atoms, molecules etc.). This is because: According to Bohr model, an orbit is a well-defined path and this path can completely be defined only if both the position and velocity of the electron are known exactly at the same time. But this is not possible according to the Heisenberg’s uncertainty principle. Thus, Bohr model contradicts the Heisenberg’s uncertainty principle . According to Bohr model, an electron is regarded as a charged particle moving in well-defined circular orbits concentric about the nucleus. The wave character of the electron is not considered. Thus, Bohr model ignores the de-Broglie dual nature of matter .
The aim of this chapter is to present some very basic principles of classical mechanics. They can help us understand the novelty of quantum theory. Classical mechanics was founded by Newton and contemporary 17th-century natural philosophers, and further developed in the 18th and 19th centuries by many physicists and mathematicians, as a result of the search for a rational, causal, and scientific explanation of the universe. In classical mechanics, real-world objects are modeled as a collection of point particles, i.e., objects with negligible size. The motion of a point particle is characterized by a small number of parameters such as its position, mass, velocity, and the forces applied to it. The position of a point particle is defined with respect to an arbitrary fixed reference point in the three- dimensional Euclidean space, which is usually chosen as the origin of some coordinate system. The velocity of a point particle is the rate of change of its position with time. The force applied to a point particle (called the external force) is the cause for the point particle x y z A to undergo a certain change in its velocity, i.e., an acceleration (Newton’s second law of motion). For the sake of simplicity, here we shall refer to a point particle or a collection of point particles simply as an object. Newton’s first law of motion states that if an object experiences no net external force, then its velocity is constant, i.e., the object is either at rest or it moves in a straight line with a constant speed. The first law of motion postulates the existence of a certain set of frames of reference called inertial reference frames, relative to which the motion of an object not subject to external forces is a straight line at a constant speed. For this reason, Newton’s first law is also referred to as the law of inertia.
The motion of macroscopic objects such as soccer balls, vehicles and planets can be well described using classical mechanics. However, classical mechanics is inadequate to describe the movements or the structure of microscopic objects such as atoms, molecules or nuclei. To properly describe the properties of microscopic objects, the theory of quantum mechanics was developed. While quantum mechanics can be applied to macroscopic objects, it turns out that for objects of large dimensions the quantum mechanical laws evolve naturally into classical mechanics. In general, solving a problem in quantum mechanics is far more difficult than solving it in classical mechanics. Therefore, the laws of classical mechanics are employed when they can be applied safely.
The results of Bohr model can be used to explain the motion of macroscopic objects or big objects (like orbiting planets and sun, falling stone etc.). These macroscopic objects have essentially a particle nature and Newtonian laws of motion can be applied on them. But it fails when applied to explain the motion of microscopic objects or small objects (like electrons, atoms, molecules etc.). This is because: According to Bohr model, an orbit is a well-defined path and this path can completely be defined only if both the position and velocity of the electron are known exactly at the same time. But this is not possible according to the Heisenberg’s uncertainty principle. Thus, Bohr model contradicts the Heisenberg’s uncertainty principle . According to Bohr model, an electron is regarded as a charged particle moving in well-defined circular orbits concentric about the nucleus. The wave character of the electron is not considered. Thus, Bohr model ignores the de-Broglie dual nature of matter .