Zero point Energy in Quantum Mechanics
Zero Point energy
 |
| Zero point Energy in Quantum Mechanics |
It is also called quantum vacuum zero-point energy and is the lowest possible energy that a quantum mechanical Physical System may have. It is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave like nature. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential well.Also Zero point energy is the energy that remains when all other energy is removed from the system. This behavior is demonstrated by, for example, liquid helium. As the temperature is lowered to absolute zero, helium remains a liquid, rather than freezing to a solid, owing to the irremovable zero-point energy of its atomic motions. (Increasing the pressure to 25 atmospheres will cause helium to freeze.) Where ''zero-point'' refers to the energy of the system at temperature T=0, or the lowest quantized energy level of a quantum mechanical system.
Harmonic Oscillator
Classically a harmonic oscillator, such as a mass on a spring,
can always be brought to rest. However a quantum harmonic oscillator does not
permit this. A residual motion will always remain due to the requirements of
the Heisenberg uncertainty principle, resulting in a zero-point energy, equal
to 1/2 hf, where f is the oscillation frequency.
This energy value is for three reasons First,
the energies are quantized, meaning that only discrete energy values
(integer-plus-half multiples of ħω) are possible; this is a general
feature of quantum-mechanical systems when a particle is confined. Second,
these discrete energy levels are equally spaced, unlike in the bhor model of the atom, or the particle in a box. Third, the lowest achievable energy (the energy of the n =
0 state, called the ground
state) is not equal to the
minimum of the classical potential well, but ħω/2 above it;
this is called Zero-point energy. Because of the zero-point energy, the
position and momentum of the oscillator in the ground state are not fixed (as
they would be in a classical oscillator), but have a small range of variance,
in accordance with the Heisenberg’s
uncertainty principle. This zero-point
energy further has important implications in quantum field theory and quantum gravity.
No comments:
Post a Comment