Quantum theory of motion Flashcards
What is a wavefunction in quantum mechanics?
It describes the probability amplitude for the position of a particle and is fundamental in calculating properties like position and momentum.
Define the term ‘quantum number’ as used in quantum mechanics.
Quantum numbers are integers that describe the energy levels of a system, influencing properties like the shape and orientation of orbitals.
What is zero-point energy?
The lowest possible energy that a quantum mechanical physical system may have; it is the energy of the ground state of the system.
Explain the principle of quantum tunnelling.
Quantum tunnelling is a phenomenon where particles move through a barrier that they classically shouldn’t be able to pass due to insufficient kinetic energy.
What does the Heisenberg Uncertainty Principle state?
It states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.
What is the significance of degeneracy in quantum systems?
Degeneracy refers to the phenomenon where two or more different quantum states share the same energy.
Define ‘particle in a box’ in quantum mechanics.
It’s a model that describes a particle free to move in a small space surrounded by impenetrable barriers.
What is the Harmonic Oscillator model in quantum mechanics?
It describes the motion of a particle in a potential well that behaves like a harmonic oscillator, where the force towards the center increases linearly with displacement.
What are nodal planes or nodes in a quantum mechanical wavefunction?
Nodes are points or planes in space where the wavefunction and therefore the probability density is zero.
Describe the concept of a two-dimensional quantum box.
A particle confined to move in a two-dimensional planar region, described by wavefunctions depending on both x and y coordinates.
How is the energy of a particle in a one-dimensional box quantized?
The energy levels are quantized and depend on the square of the quantum number, inversely proportional to the square of the box’s length.
What determines the number of nodes in the wavefunction of a quantum particle in a box?
The number of nodes is one less than the quantum number (n-1).
How does quantum tunnelling contrast with classical predictions?
Classically, particles with insufficient energy cannot surpass a barrier, while in quantum mechanics, there is a probability for particles to tunnel through barriers despite insufficient energy.
How do energy levels change with increasing quantum number in a harmonic oscillator?
Energy levels are equally spaced, increasing linearly with the quantum number.
What role does the reduced mass play in the vibrational motion of a molecule?
The reduced mass is used to calculate the natural frequency of vibration for the harmonic oscillator model, influencing the vibrational energy levels.
