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Exercise:
Calculate the phase and group velocity of the de Broglie wave for a proton with kinetic energy EkO. Verify that the product of phase and group velocity has the expected value.

Solution:
The phase velocity is v_p fracEp fracE_+sscEkinp fracE_+sscEkinsqrtm sscEkin fracE_+sscEkinsqrt fracE_c^sscEkin vpF fracErest+EksqrttimesEresttimesEktimes c resultvpS The group velocity is equal to the particle velocity: v_g vgF sqrtfractimesEkErest c resultvgS The product of phase and group velocity is v_p v_g productF resultproductS The deviation is due to the approximation as a non-relativistic particle.
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Exercise:
Calculate the phase and group velocity of the de Broglie wave for a proton with kinetic energy EkO. Verify that the product of phase and group velocity has the expected value.

Solution:
The phase velocity is v_p fracEp fracE_+sscEkinp fracE_+sscEkinsqrtm sscEkin fracE_+sscEkinsqrt fracE_c^sscEkin vpF fracErest+EksqrttimesEresttimesEktimes c resultvpS The group velocity is equal to the particle velocity: v_g vgF sqrtfractimesEkErest c resultvgS The product of phase and group velocity is v_p v_g productF resultproductS The deviation is due to the approximation as a non-relativistic particle.
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quantum physics
Tags
energy, group velocity, momentum, phase velocity, proton
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(2, default)
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Language
ENG (English)
Type
Calculative / Quantity
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