- #1
Happiness
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- 30
Why so?
Quoted from Quantum Physics 3rd ed. by Stephen Gasiorowicz, p. 26.
It was explaining why we ignore the terms with exp[iwt] when adding plane waves to form a wave packet:
Try applying the energy operator ##\hat H = i\hbar \frac{\partial }{\partial t}## to the wavefunction with ##\exp(i\omega t)##. In fact the time-exponential factor arises from the application of time evolution operator ##\exp(-i\hat H t/\hbar)##, thus it makes perfect sense that one should use ##\exp(-i\omega t)## since the kinetic energy is positive.Happiness said:Why so?
The negative kinetic energy of the waveform exp[iwt] is a result of the complex nature of the exponential function. The negative sign in front of the kinetic energy term is a mathematical convention used to indicate the direction of energy flow. It does not have any physical significance and does not affect the overall behavior or properties of the waveform.
Yes, negative kinetic energy is physically possible and is often encountered in quantum mechanics and other areas of physics. It is a mathematical concept used to describe the direction and magnitude of energy flow, and does not violate any physical laws.
No, the negative kinetic energy of exp[iwt] does not affect the overall energy of a system. In fact, the total energy of a system is always positive, as it represents the sum of potential and kinetic energies. The negative sign is simply a convention used to indicate the direction of energy flow.
The negative kinetic energy of exp[iwt] does not violate the principle of energy conservation. In a closed system, energy can neither be created nor destroyed, but it can change forms. The negative kinetic energy of exp[iwt] is simply a way of describing the transfer of energy within a system.
Yes, negative kinetic energy has practical applications in various fields, such as quantum mechanics, electromagnetism, and thermodynamics. It is used to describe the behavior of particles and energy flow in these systems and helps in understanding and predicting their properties and interactions.