Group velocity of a constant-coefficient envelope

The first set is the low-speed constant-B envelope. The full isotropic gapped branch with E=ℏω and P=ℏk gives vg=c²P/E=v. Momentum-dependent B requires its derivatives.

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ASD-WEB-QM-010

E_{\rm kin}=\frac{p_iB_{ij}p_j}{2m_0},\quad p_i=\hbar k_i,\quad v_{g,i}=\frac{B_{ij}p_j}{m_0};\qquad B=I:\ \mathbf v_g=\frac{c^2\mathbf k}{\omega}=\frac{c^2\mathbf P}{E}=\mathbf v

The first set is the low-speed constant-B envelope. The full isotropic gapped branch with E=ℏω and P=ℏk gives vg=c²P/E=v. Momentum-dependent B requires its derivatives.
Chapter reference: Ch. 5 (5.2.14) · ASD-BOOK-ddbade997b45

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Ch. 5 (5.2.14)

The first set is the low-speed constant-B envelope. The full isotropic gapped branch with E=ℏω and P=ℏk gives vg=c²P/E=v. Momentum-dependent B requires its derivatives.

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Selected channel and stated initial/boundary conditions; action/energy matching retained
Continuum, slow-envelope and detector approximations kept at their respective levels

Source locators: p1876 · p1879 · p1880 · p1882 · p1884 · p1900

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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QM-0accdcbe7725 · Ch. 5 (5.2.14)

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