Table of Contents
Why does Gaussian wave packet spread?
A wave packet naturally spreads because it contains waves of different momenta and hence different velocities. Wave packets that are very localized in space spread rapidly.
What are Gaussian wave packet in quantum mechanics?
A Gaussian wave packet centered around at time with an average initial momentum can be represented by the wavefunction . At , the Gaussian probability distribution represents a minimum uncertainty wave packet with , but the product increases when .
Why do wave packets spread?
As time passes the initial uncertainty in position is compounded by the uncertainty in momentum. So, as an electron moves the uncertainty in position increases. This change in uncertainty is represented in Quantum Motion by a change in the wave function. As time passes, the wave function spreads out.
What is wave Group How does the concept of wave group leads to uncertainty?
The uncertainty principle arises from the wave-particle duality. Every particle has a wave associated with it; each particle actually exhibits wavelike behaviour. So a strictly localized wave has an indeterminate wavelength; its associated particle, while having a definite position, has no certain velocity.
What is Gaussian wave function?
In summary, the Gaussian density function, (3.63), contains a set of wave numbers clustered around the carrier wave number, . For a uniform distribution, σ x → ∞ , thus k → 0 . Conversely, infinitely many wave numbers are needed to describe a sharp Gaussian, i.e. as σ x → 0 .
What is a Gaussian wave function?
What are the properties of Gaussian wave packet?
The probability distribution stays Gaussian for all t. As the momentum amplitudes become complex, its width σx√1+ω2σt2 increases with a characteristic time 1/ωσ=2mσ2x/ℏ, and its center moves with the group velocity vg=ℏk0/m.
What is a quantum packet?
quantum, in physics, discrete natural unit, or packet, of energy, charge, angular momentum, or other physical property. These particle-like packets of light are called photons, a term also applicable to quanta of other forms of electromagnetic energy such as X rays and gamma rays.
Why does the Gaussian packet spread?
Remember that the gaussian packet describes the probability distribution of the particle. When the packet spreads it doesn’t mean the particle is in some sense swelling up and spreading out, it means the probability of finding the particle is spreading out. The reason for this is that the gaussian has a spread…
How does the Gaussian wavepacket spread in an oscillator?
The Gaussian wavepacket only spreads in the free Schrodinger equation. It doesn’t spread in the case where you have a harmonic oscillator, and the Gaussian width is equal to that of the ground state wavefunction. For other Gaussians in an oscillator, the width oscillates, growing and shrinking.
What determines the spread of a free field wave packet?
Spreading of the free field wave packet. The spreading of the wave-function is inversely proportional to the frequency (the phase change rate in time) of the particle, Higher mass particles spread slower. The spreading of the wave-function is proportional to the square of the momentum spread.
Does the wave-packet spread in momentum space?
The wave-packet would not spread in the case of a single v such as in the case of a massless particle which is represented by a wave-function which moves unchanged at the speed of light. However, a localized field with a Gaussian shape has (via the Fourier transform) a Gaussian distribution of p in momentum space.