Quantum mechanics part -1

                                         Quantum mechanics

Quantum physics is the study of matter and energy at the most fundamental level. It aims to uncover the properties and behaviors of the very building blocks of nature.

While many quantum experiments examine very small objects, such as electrons and photons, quantum phenomena are all around us, acting on every scale. However, we may not be able to detect them easily in larger objects. This may give the wrong impression that quantum phenomena are bizarre or otherworldly. In fact, quantum science closes gaps in our knowledge of physics to give us a more complete picture of our everyday lives.

Quantum discoveries have been incorporated into our foundational understanding of materials, chemistry, biology, and astronomy. These discoveries are a valuable resource for innovation. The time evolution of a quantum state is described by the Schrodinger equation:

Here denotes the Hamiltonian, the observable corresponding to the total energy of the system, and is the reduced Planck constant. The constant is introduced so that the Hamiltonian is reduced to the classical Hamiltonian in cases where the quantum system can be approximated by a classical system; the ability to make such an approximation in certain limits is called the correspondence principle.

The solution of this differential equation is given by

${\displaystyle �(�)={�}^{-���/\hslash }�(0).}$

The operator is known as the time-evolution operator and has the crucial property that it is unitary. This time evolution is determined in the sense that – given an initial quantum state ${\displaystyle �(0)}$  – it makes a definite prediction of what the quantum state ${\displaystyle �(�)}$ will be at any later time

The Origins of Quantum Physics:

• Superposition: This is a term used to describe an object as a combination of multiple possible states at the same time. A superposed object is analogous to a ripple on the surface of a pond that is a combination of two waves overlapping. In a mathematical sense, an object in superposition can be represented by an equation that has more than one solution or outcome.

• Uncertainty principle: This is a mathematical concept that represents a trade-off between complementary points of view. In physics, this means that two properties of an object, such as its position and velocity, cannot both be precisely known at the same time. If we precisely measure the position of an electron, for example, we will be limited in how precisely we can know its speed.

• Entanglement: This is a phenomenon that occurs when two or more objects are connected in such a way that they can be thought of as a single system, even if they are very far apart. The state of one object in that system can't be fully described without information on the state of the other object. Likewise, learning information about one object automatically tells you something about the other and vice versa.

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Quantum mechanics video lecture