Most Important Quantum Mechanics questions asked in Phd Physics Interview

 1) Explain what is Quantum Physics?

Quantum physics is the study of how matter and energy behave at the molecular, nuclear, atomic, and even microscopic levels. Quantum physics is required if you want to understand how electrons move through a computer chip, how photons of light are converted to electrical current in solar panels or magnify themselves in lasers, or even just how the sun continues to burn.

2) What is the significance of the name ”quantum physics”?

Albert Einstein postulated that light can only be absorbed in specific "packets" while explaining the photoelectric phenomenon in 1905. He proposed that the photon, or "quanta," as it was then known, is an elementary part of light. This had a significant impact on the emergence of a new physics.

3) So everything has quanta, and that's the fundamental idea of quantum physics?

Actually, no. It's not even true, really. Taken as an example, the energy levels of an H-atom can be determined. The assertion that "energy is quantized", however, is false. Now, if we take a different atom, we find different energy levels; but, the levels we actually find do not reflect some property of energy that exists everywhere; rather, they are unique to the system in question. By the way, similar events can also occur in classical physics. For instance, a cord can only vibrate at specific frequencies. There is no inherent unit of frequency in classical physics, yet different cords can vibrate at a wide range of different frequencies.

4) Then what is the essence of quantum physics? What makes it so different from classical physics?

The concept of an object is an odd mixture of both particles and waves. If given comprehensive knowledge of the past, we can only make probabilistic judgments of the future.

Two bombs with identical fuses would detonate simultaneously in accordance with classical physics. According to quantum physics, two radioactive atoms that are completely similar can and usually do explode at very different times. Despite the fact that they are similar, two uranium-238 atoms will typically experience radioactive decay separated by billions of years.

Physics experts frequently utilize a rule to distinguish between conventional and quantum physics. It is quantum physics if the Plank constant occurs in the equation. If not, classical physics applies.

Even though many specifics have yet to be worked out, the majority of scientists think that quantum physics is the correct theory. When the quantum features are veiled, one can infer classical physics from quantum physics.  That fact is called the "correspondence principle."

In quantum mechanics, even if you have full knowledge of a system, the outcomes of certain measurements will be impossible to predict.

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Between Classical and Quantum Theories, there are significant differences.

a. In classical theory, a body always chooses the least action path and there is only one path. In Quantum theory, a particle also always chooses the least action path and it chooses multiple least action paths simultaneously.

b. If there are 9 boxes and 10 pigeons, then at least one box will end up with two pigeons. This is in Classical Theory. No such thing happens in Quantum Theory. With just two boxes, we can transmit an infinite number of electrons.

c. We can determine the position and velocity of a particle simultaneously with great accuracy in Classical Physics. Quantum Physics follows the Heisenberg Uncertainty Principle.

d. Classical Physics is applicable to macroscopic particles. Microscopic particles are subject to quantum mechanics.

5) So quantum physics must be a probability theory? 

According to quantum physics, probability is not a short cut and is actually built into the narrative from the very beginning. At very short distances, quantum particles and the corresponding wave functions control everything in the cosmos.  The odds of finding a specific outcome (like the location of a particular atom ten seconds from now) are derived from the famous wave function—symbolized by Ψ (the Greek letter psi).

The phrase "wave function" refers to the fact that the probability of finding an atom at any particular position is best represented in terms of the crests and troughs of a wave, much like how ripples and waves might have high and low spots on the surface of a pond. These waves can combine to have a greater impact, increasing the likelihood of certain events, or they can interfere with one another, reducing the likelihood of seeing any events at all. Some of the less understandable aspects of quantum physics result from this. For instance, quantum particles are capable of performing other allegedly "miraculous feats," which defy both our expectations and those of classical physics.

6) What exactly is the uncertainty principle?

The uncertainty principle says that we cannot measure the position (x) and the momentum (p) of a particle with absolute precision. The more accurately we know one of these values, the less accurately we know the other. 

According to the uncertainty principle, it is impossible to determine a particles's precise position(x) and momentum(p). One of these values accuracy corresponds to how well we understand the other.

Consequences of the Uncertainty Principle

a. The most important consequence of uncertainty principle is the dual nature of matter.

b. In the dual nature, it is not possible to determine the wave and particle properties exactly at the same time.

c. The complementarity principle states that the wave and particle aspects of matter are complementary, instead of being contradictory.

d. This principle suggests that the consideration of particle and light natures is necessary to have a complete picture of the same system.

7) Explain what is Wave-Particle duality?

Wave-particle duality describes a fundamental characteristic of matter where it behaves like a particle sometimes and a wave other times.

As the wave propagates, where is the particle? Well, we don’t know for sure. It is situated in the region of space whose dimension is equal to the distribution of the wavelengths that constitute its wave. This is known as Heisenberg’s uncertainty principle.

At the turn of the century, when the photoelectric effect provided the conclusive evidence of a particle nature as well, the evidence supporting the depiction of light as waves was well established.

However, when the de Broglie hypothesis and subsequent investigations by Davisson and Germer revealed the electron's wave nature, the particle characteristics of electrons were well established.

Waves can be used to describe the majority of the observable occurrences with light. The photoelectric effect, however, indicated that light may be made up of  particles. Then electrons too were found to exhibit dual natures.

8) Explain what is Quantum tunneling?

When a particle is able to pass through a potential energy barrier with an energy greater than its own kinetic energy, this process is known as Tunneling in quantum mechanics. This remarkable characteristic of microscopic particles is crucial in the explanation of a number of scientific processes, including radioactive decay. The Scanning Tunneling Microscopic (STM), which had a significant impact on chemical, biological, and material science studies was also developed using the tunneling concept.

The phenomenon of tunneling has many important applications.  It explains a sort of radioactive decay, for instance, in which a nucleus emits an alpha particle (a helium nucleus). The alpha particle is constrained before the disintegration by a potential, according to the quantum theory proposed separately in 1928 by George Gamow, Ronald W. Gurney, and Edward Condon. The energy E of the released alpha particle and the typical lifetime of the nucleus before decay can both be determined for a specific nuclear species. The probability of tunneling through the barrier is measured by the lifetime of the nucleus; the shorter the lifetime, the greater the probability.

9) Explain what is Quantum entanglement?

One of the most strange occurrences that can be observed when things are extremely small or within the quantum realm is quantum entanglement. No matter how far apart two or more particles are in space, their states remain connected when they join up in a specific way. That indicates that they exist in a single, shared quantum state. Therefore, regardless of their distance from one another, observations of one of the particles can automatically reveal information about the other entangled particles. And any change to one of these particles will inevitably have an effect on the others in the entangled system.

10) How can you create Quantum Entanglement?

Particles can become entangled in numerous ways. The particles can be cooled and positioned so closely together that their quantum states, which describe the position's uncertainty, overlap, rendering it hard to discriminate between one particle and another.

Another approach is to rely on a subatomic process, such as nuclear decay, that generates entangled particles on its own. According to NASA, entangled pairs of photons, or light particles, can also be produced by dividing a single photon into two, or by mixing two pairs of photons in a fiber-optic cable.

11) What could be the application of Quantum Entanglement?

Cryptography is arguably where quantum entanglement is employed the most frequently. In this case, a sender and a receiver create a secure communication link that consists of entangled particle pairs, claims Caltech Magazine. The entangled particles are used by the transmitter and receiver to create private keys that are only known to them and can be used to encrypt their communications. Because measuring an entangled particle affects its state, entanglement breaks if someone intercepts the signal and tries to read the secret keys. The sender and the recipient will be aware that their communications have been compromised as a result.

Quantum computing, in which numerous particles are entangled and can cooperate to solve a number of significant, challenging problems, is another application of entanglement. For instance, a quantum computer with just 10 qubits (quantum bits) may simulate 210 conventional bits' worth of memory.

12) What is Hilbert Space? What is its significance in quantum mechanics?

In quantum Mechanics, a vector in a Hilbert space- a complex vector space with an inner product represents the state of a physical system.

When referring to an infinite-dimensional inner product space with  the quality of being complete or closed, the phrase "Hilbert space, is frequently used. However, the term is now commonly utilized, as in these notes, in a form that includes finite-dimensional spaces, which by definition satisfy the condition of completeness. 

Significance-

The presence of Hilbert Space in a mathematical calculation indicates the occurrence of points in infinite sequences. These points constitute real numbers of the mathematical domain for the benefit of calculation. These points are summable by nature and are expressed as infinite series. The Hilbert Space can be related to Euclidean Space with an infinite series of points. The points in the inner space of the Hilbert Space are expressed using the concept of Vector Space. The vector calculations of the Hilbert Space can be expressed using calculations of dot products. The inner product space of the Hilbert Space is defined by the norm of an inner product.

14) What are Hermitian operators?

 A Hermitian or self-adjoint operator A is defined by the property that A = A†, so it is a normal operator. It is the quantum analog of a real (as opposed to a complex) number. Its eigenvalues αj are real numbers.

 For a finite-dimensional Hilbert space, which is all we are concerned,the terms "Hermitian" and "self-adjoint" have the same meaning; the distinction is significant only for infinite-dimensional spaces.

Hermitian operators in quantum mechanics are used to represent physical variables, quantities such as energy, momentum, angular momentum, position, and the like. The operator representing the energy is the Hamiltonian H.

Significance- 

 Hermitian operators play an integral role in quantum mechanics due to two of their properties. First, their eigenvalues are always real. This is important because their eigenvalues correspond to physical properties of a system, which cannot be imaginary or complex. Second, their eigenfunctions are orthonormal, which greatly simplifies many quantum mechanical problems.

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