Skip to main content
Physics

Return to Question

replaced http://physics.stackexchange.com/ with https://physics.stackexchange.com/
Source Link
Community Bot
Community Bot
  • 1

This question is based on this questionthis question asked in physics SE. In this question, they say that phase velocity greater than velocity of light. Ok, greater than velocity of light for phase velocity is acceptable. But group velocity must be $\leq{c}$ . But in my knowledge, for a quantum free particle, phase velocity $$V_p=\frac{\omega}{k}=\frac{p}{2m}$$ and group velocity $$V_g=\frac{d\omega}{dk}=\frac{p}{m} .$$ Obviously $$V_g=2V_p.$$ But how this is possible? This means group velocity also greater than velocity of light, and is pure nonsense. Where is the mistake happened to me?

This question is based on this question asked in physics SE. In this question, they say that phase velocity greater than velocity of light. Ok, greater than velocity of light for phase velocity is acceptable. But group velocity must be $\leq{c}$ . But in my knowledge, for a quantum free particle, phase velocity $$V_p=\frac{\omega}{k}=\frac{p}{2m}$$ and group velocity $$V_g=\frac{d\omega}{dk}=\frac{p}{m} .$$ Obviously $$V_g=2V_p.$$ But how this is possible? This means group velocity also greater than velocity of light, and is pure nonsense. Where is the mistake happened to me?

This question is based on this question asked in physics SE. In this question, they say that phase velocity greater than velocity of light. Ok, greater than velocity of light for phase velocity is acceptable. But group velocity must be $\leq{c}$ . But in my knowledge, for a quantum free particle, phase velocity $$V_p=\frac{\omega}{k}=\frac{p}{2m}$$ and group velocity $$V_g=\frac{d\omega}{dk}=\frac{p}{m} .$$ Obviously $$V_g=2V_p.$$ But how this is possible? This means group velocity also greater than velocity of light, and is pure nonsense. Where is the mistake happened to me?

added 6 characters in body; edited tags; edited title
Source Link
Qmechanic ♦
Qmechanic ♦
  • 212.7k
  • 48
  • 589
  • 2.3k

confusion Confusion in phase and group velocity

This question is based on this question asked in physics SE. In this question, they say that phase velocity greater than velocity of light. Ok, greater than velocity of light for phase velocity is acceptable. But group velocity must be $\leq{c}$ . But in my knowledge, for a quantum free particle, phase velocity $V_p=\frac{\omega}{k}=\frac{p}{2m}$$$V_p=\frac{\omega}{k}=\frac{p}{2m}$$ and group velocity $V_g=\frac{d\omega}{dk}=\frac{p}{m}$ .$$V_g=\frac{d\omega}{dk}=\frac{p}{m} .$$ Obviously $V_g=2V_p$.$$V_g=2V_p.$$ But how this is possible? This means group velocity also greater than velocity of light, and is pure nonsense. Where is the mistake happened to me?

confusion in phase and group velocity

This question is based on this question asked in physics SE. In this question, they say that phase velocity greater than velocity of light. Ok, greater than velocity of light for phase velocity is acceptable. But group velocity must be $\leq{c}$ . But in my knowledge, for a quantum free particle, phase velocity $V_p=\frac{\omega}{k}=\frac{p}{2m}$ and group velocity $V_g=\frac{d\omega}{dk}=\frac{p}{m}$ . Obviously $V_g=2V_p$. But how this is possible? This means group velocity also greater than velocity of light, and is pure nonsense. Where is the mistake happened to me?

Confusion in phase and group velocity

This question is based on this question asked in physics SE. In this question, they say that phase velocity greater than velocity of light. Ok, greater than velocity of light for phase velocity is acceptable. But group velocity must be $\leq{c}$ . But in my knowledge, for a quantum free particle, phase velocity $$V_p=\frac{\omega}{k}=\frac{p}{2m}$$ and group velocity $$V_g=\frac{d\omega}{dk}=\frac{p}{m} .$$ Obviously $$V_g=2V_p.$$ But how this is possible? This means group velocity also greater than velocity of light, and is pure nonsense. Where is the mistake happened to me?

Source Link
Muhsin Ibn Al Azeez
Muhsin Ibn Al Azeez
  • 664
  • 1
  • 11
  • 22

confusion in phase and group velocity

This question is based on this question asked in physics SE. In this question, they say that phase velocity greater than velocity of light. Ok, greater than velocity of light for phase velocity is acceptable. But group velocity must be $\leq{c}$ . But in my knowledge, for a quantum free particle, phase velocity $V_p=\frac{\omega}{k}=\frac{p}{2m}$ and group velocity $V_g=\frac{d\omega}{dk}=\frac{p}{m}$ . Obviously $V_g=2V_p$. But how this is possible? This means group velocity also greater than velocity of light, and is pure nonsense. Where is the mistake happened to me?