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aleemudasir
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According to de-broglie's equation λ=h/p, so a/c to this equation what would be wavelength of particle at zero speed?
Bill_K said:aleemudasir, I think you know the answer, but I'll say it anyway. Infinity. As p gets smaller and smaller, the deBroglie wavelength gets longer and longer.
Since an actual object will be in practice confined to some finite volume, this implies that p can never go all the way to zero. And so a real object can never be completely at rest.
Bill_K said:You cannot have a ball of mass 1 kg with v = 0. This would imply that you have absolutely no idea where it is, it's just as likely to be somewhere on alpha centauri as it is on the table. If you do observe the ball sitting on the table then its deBroglie wavelength λ must be at least as small as the table, implying that the object has a small nonzero velocity ~ h/mλ.
chill_factor said:a ball is not a quantum mechanical object. instead we can think about it as a collection of polymer molecules which are quantum mechanical and use statistical physics.
there are N (where N is a gigantic number like 10^23) polymer molecules bound to their equilibrium positions within the ball by electrostatic van der Waals forces. due to this potential, their wavefunctions are confined to finite volumes with a finite momentum. they oscillate about those equilibrium positions due to thermal energy (but also due to the zero point energy). because this motion is thermal, it is approximately uniform in magnitude (follows the Boltzmann distribution in this case) and random in direction, and thus the net displacement is zero for a very large collection of molecules.
The net force is what we perceive to be a motionless ball.
Let me just say it again: a ball is made up of polymers, a ball is not quantum mechanica, the polymer molecules that make up the ball are quantum mechanical.
chill_factor said:a ball is not a quantum mechanical object. instead we can think about it as a collection of polymer molecules which are quantum mechanical and use statistical physics.
there are N (where N is a gigantic number like 10^23) polymer molecules bound to their equilibrium positions within the ball by electrostatic van der Waals forces. due to this potential, their wavefunctions are confined to finite volumes with a finite momentum. they oscillate about those equilibrium positions due to thermal energy (but also due to the zero point energy). because this motion is thermal, it is approximately uniform in magnitude (follows the Boltzmann distribution in this case) and random in direction, and thus the net displacement is zero for a very large collection of molecules.
The net force is what we perceive to be a motionless ball.
Let me just say it again: a ball is made up of polymers, a ball is not quantum mechanica, the polymer molecules that make up the ball are quantum mechanical.
chill_factor said:a ball is not a quantum mechanical object. instead we can think about it as a collection of polymer molecules which are quantum mechanical and use statistical physics.
there are N (where N is a gigantic number like 10^23) polymer molecules bound to their equilibrium positions within the ball by electrostatic van der Waals forces. due to this potential, their wavefunctions are confined to finite volumes with a finite momentum. they oscillate about those equilibrium positions due to thermal energy (but also due to the zero point energy). because this motion is thermal, it is approximately uniform in magnitude (follows the Boltzmann distribution in this case) and random in direction, and thus the net displacement is zero for a very large collection of molecules.
The net force is what we perceive to be a motionless ball.
Let me just say it again: a ball is made up of polymers, a ball is not quantum mechanica, the polymer molecules that make up the ball are quantum mechanical.
aleemudasir said:But what if instead of a ball having mass m I have an electron, and the rest of the problem is same as described earlier!
Whovian said:Electrons don't have temperature. Temperature is the measure of the average kinetic energy of particles in an object that doesn't contribute to its velocity. In the case of an electron, the kinetic energy (in an arbitrary reference frame) all contributes to the electron's total velocity, therefore it's 0. (Or at least, I think. This is a bit less rigorous than I would like, but it works.)
Individual particles can have temperature, the average would just be x/1. Kinetic energy is equivalent to thermal energy, so...Whovian said:Electrons don't have temperature. Temperature is the measure of the average kinetic energy of particles in an object that doesn't contribute to its velocity.
hefty said:Hi Chill Factor,
Technically speaking, It's also true that a small ball has a chance to behave as a quantum object, right?
Meaning that it may totally disappear and appear somewhere else for example. (Probably We need to wait longer than the 1 zillion times the life of our universe, but it may happen, right?
Regards
Hefty
scijeebus said:Not only that, but treating a quantum particle merely as a wave itself is sort of out-dated. You might want to look into quantum field theory where particles can be described using the harmonic oscillations of fields.
The wavelength of matter waves at speed equal to zero is significant because it is a fundamental property of matter and is related to the momentum and energy of particles. It also plays a crucial role in understanding quantum mechanics and the behavior of particles at the atomic and subatomic level.
Yes, the wavelength of matter waves at speed equal to zero can be measured using sophisticated techniques such as electron diffraction or neutron diffraction. These methods involve passing a beam of particles through a crystal or other material and analyzing the diffraction pattern to determine the wavelength.
The wavelength of matter waves at speed equal to zero is significantly smaller than the wavelength of light. This is because matter waves have much smaller momenta and energies compared to light waves. Additionally, matter waves are affected by the mass and velocity of particles, while light waves are not.
Yes, the wavelength of matter waves at speed equal to zero can be changed by altering the momentum or energy of the particles. This can be achieved by applying external forces or by changing the properties of the material through which the particles are passing.
The wavelength of matter waves at speed equal to zero is related to the uncertainty principle, which states that the more accurately we know the position of a particle, the less accurately we can know its momentum, and vice versa. The wavelength of matter waves is inversely proportional to the momentum of particles, so a smaller wavelength (i.e. more accurately known position) means a larger uncertainty in momentum.