Introductory Wave Mechanics
Introductory Wave Mechanics
Need of Quantum Theory ( Black body radiation )
Important equaiton to be remember:
- $$u(\nu, T)= \frac{8\pi\nu^2}{c^3}\times$$ <...}
Introductory Wave Mechanics
Inadequacies of classical Mechanics
Inadequacies of classical Mechanics:
- It could not explain the spectr...}
Introductory Wave Mechanics
Wave-Matter duality of radiation
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According to Plank's theory of radiation energy of photon of frequency \(\nu\) is given...}
Introductory Wave Mechanics
de-Broglie Wavelength of relativistic particle
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The de-Broglie wavelength of particle is given by,
$$\lambda=\frac{h}{p}$$
<...}
Introductory Wave Mechanics
Calculation of de-Broglie wavelength of neutrino, diatomic gas and poly-atomic gas
- de-Broglie wavelength of poly-atomic gas $$=\frac{h}{\sqrt{2mKT}}$$
- de-Brogli...}
Introductory Wave Mechanics
Phase velocity and group velocity
- The velocity of a complete wave profile is known as phase velocity or it is also defined as...}
Introductory Wave Mechanics
Derivation for Group velocity
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$$= A sin\biggl[\biggl(k+\frac{\Delta k}{2}\biggr)x-\biggl(\omega+\frac{\Delta \omega}{...}
Introductory Wave Mechanics
Relation between group velocity and particle velocity
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\(\Delta x\cdot \Delta P_x= h<\frac{hbar}{2}\) from the concept of wave packet.
...}
Introductory Wave Mechanics
Superposition of plane waves
- $$\psi (x,t)= \sum_{i=1}^\infty A_i e^{i(k_i x- \omega_i t)}\dotsm(1)$$
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...}
Introductory Wave Mechanics
Particles wave packet spreads in time
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$$\psi(x,t)= \int_{-\infty}^\infty e^{-\sigma(k-k_0)^2} e^{i(kx-\omega(k_0)t-(k-k_0)tv_...}