GATE Physics Exam > GATE Physics Videos > Quantum Mechanics for GATE > Lecture 10: Free Particle Quantum Mechanics
Lecture 10: Free Particle Quantum Mechanics Video Lecture | Quantum Mechanics for GATE - GATE Physics
FAQs on Lecture 10: Free Particle Quantum Mechanics Video Lecture - Quantum Mechanics for GATE - GATE Physics
| 1. What is a free particle in quantum mechanics? |  |
Ans. In quantum mechanics, a free particle is a particle that is not subjected to any external forces or potentials. This means that the particle's energy is determined solely by its momentum.
| 2. How is the wave function of a free particle described in quantum mechanics? | |
Ans. The wave function of a free particle in quantum mechanics is described by a plane wave. This plane wave represents the probability amplitude of finding the particle at a certain position in space.
| 3. How does the energy of a free particle in quantum mechanics relate to its momentum? | |
Ans. In quantum mechanics, the energy of a free particle is related to its momentum through the de Broglie relation, which states that the wavelength of a particle is inversely proportional to its momentum. This relationship is given by the equation E = (p^2)/(2m), where E is the energy, p is the momentum, and m is the mass of the particle.
| 4. What is the uncertainty principle in quantum mechanics and how does it apply to free particles? | |
Ans. The uncertainty principle in quantum mechanics states that there is a fundamental limit to the precision with which certain pairs of properties of a particle, such as position and momentum, can be known simultaneously. For free particles, this means that the more accurately we know the momentum of a particle, the less precisely we can know its position, and vice versa.
| 5. How does the concept of wave-particle duality apply to free particles in quantum mechanics? | |
Ans. The concept of wave-particle duality in quantum mechanics states that particles, such as electrons, can exhibit both wave-like and particle-like behavior. For free particles, this means that they can be described by both wave functions, which represent their probability amplitudes, and classical particles with well-defined positions and momenta.
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