# Wave-packets with opposite momenta.

• alemsalem
In summary, it is possible to prepare a particle with a wave-packet having momenta in opposite directions by sending it at a potential barrier with specific height and width. The resulting wave function will have a portion moving away from the barrier in the original direction and a portion moving away in the opposite direction. Regarding the question about the phase velocity of an electron in a microwave, it is not higher than the speed of light but is roughly half of the particle's velocity.

#### alemsalem

Is it possible to prepare a particle with a wave-packet having momenta in opposite directions,
so that you have two localized packets moving away from each other (for a single particle)?

Sure. Send a particle at a potential barrier with a height and width such that the particle has some probability to tunnel through, and some probability to be reflected. After encountering the barrier, a portion of the particle's wave function will be on the other side of the barrier traveling in the original direction, while a different portion will be moving away from the barrier opposite the original direction of motion, having been reflected.

is phase velocity of electron in microwave sense is greater than speed of light?

is phase velocity of electron is greater than speed of light.?

i think its very complicated things..

its not higher than the speed of light, I think its half the particle's velocity (group velocity)

Vphase = (h*omega)/(h k) = (p^2/2m)/p = p/2m = v/2 roughly speaking..

## 1. What are wave-packets with opposite momenta?

Wave-packets with opposite momenta are a type of quantum mechanical phenomenon in which two particles with opposite momenta are entangled and can exhibit wave-like behavior. This means that they can be in multiple places at once and can interfere with each other.

## 2. How are wave-packets with opposite momenta created?

Wave-packets with opposite momenta can be created using a process called pair production. This involves creating two particles with opposite momenta from a single high-energy photon. Another method is using a quantum entanglement process, where two particles are prepared in a way that their momenta are opposite to each other.

## 3. What is the significance of wave-packets with opposite momenta?

Wave-packets with opposite momenta have significant implications in quantum mechanics and can help us better understand the nature of particles and their wave-like behavior. They also have potential applications in quantum information processing and quantum communication.

## 4. How do wave-packets with opposite momenta behave differently from regular particles?

Unlike regular particles, wave-packets with opposite momenta exhibit wave-like behavior and can be in multiple places at once. They are also entangled, meaning that any changes to one particle will affect the other, regardless of the distance between them.

## 5. Can wave-packets with opposite momenta be observed in real life?

Yes, wave-packets with opposite momenta have been observed in experiments using high-energy particle accelerators and quantum entanglement setups. However, their behavior is still not fully understood and further research is being conducted to better understand and utilize this phenomenon.