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Quantum Physics Summary Notes
(Exam-Oriented)
1. Introduction to Quantum Physics
Quantum physics deals with phenomena at atomic and subatomic scales, where classical physics fails. It emerged from failures of classical theories like the ultraviolet catastrophe in blackbody radiation. Max Planck (1900) proposed energy is quantized: E=nhν E = nh\nu E=nhν, where n n n is integer, h h h is Planck's constant (6.626×10−34 6.626 \times 10^{-34} 6.626×10−34 J s), ν \nu ν is frequency.
The blackbody radiation spectrum shows intensity vs. wavelength, with classical Rayleigh-Jeans law diverging at short wavelengths, resolved by Planck's quantum hypothesis.
britannica.com Blackbody radiation | Definition & Facts | Britannica
2. Photoelectric Effect
Albert Einstein (1905) explained photoelectric effect: light ejects electrons from metal if frequency exceeds threshold ν0 \nu_0 ν0. Energy of photon: E=hν E = h\nu E=hν. Kinetic energy of electron: Kmax=hν−ϕ K_{max} = h\nu - \phi Kmax=hν−ϕ, where ϕ=hν0 \phi = h\nu_0 ϕ=hν0 is work function. Key points: Intensity affects number of electrons, not energy; instantaneous emission; supports particle nature of light.
(Note: No image returned for photoelectric effect; visualize light beam on metal surface emitting electrons.)
3. Wave-Particle Duality
Louis de Broglie (1924) proposed matter has wave properties: wavelength λ=hp \lambda = \frac{h}{p} λ=ph, where p p p is momentum. Applies to electrons, protons, etc. Confirmed by electron diffraction.
The double-slit experiment demonstrates duality: Particles like electrons create interference patterns, behaving as waves when not observed, but as particles when detected at slits.
kaiserscience.wordpress.com Heisenberg Uncertainty Principle « KaiserScience
5. Schrödinger Equation
Erwin Schrödinger (1926) formulated wave mechanics. Time-dependent: iℏ∂ψ∂t=H^ψ i\hbar \frac{\partial \psi}{\partial t} = \hat{H} \psi iℏ∂t∂ψ=H^ψ, where ψ \psi ψ is wave function, H^ \hat{H} H^ is Hamiltonian (−ℏ22m∇2+V -\frac{\hbar^2}{2m} \nabla^2 + V −2mℏ 2 ∇2+V).
Time-independent for stationary states: H^ψ=Eψ \hat{H} \psi = E \psi H^ψ=Eψ. Probability density: ∣ψ∣2 |\psi|^2 ∣ψ∣2. Normalization: ∫∣ψ∣2dV= \int |\psi|^2 dV = 1 ∫∣ψ∣2dV=1.
The equation describes evolution of quantum states.
mbhushal10289.medium.com The Uncertainty Principle and Schrodinger Equation | by Manish Bhusal | Medium
6. Quantum Model of Hydrogen Atom
Niels Bohr (1913) model: Electrons in discrete orbits, angular momentum quantized: L=nℏ L = n\hbar L=nℏ. Energy levels: En=−13.6n2 E_n = -\frac{13.6}{n^2} En=−n213.6 eV, n=1,2,… n = 1,2,\dots n=1,2,….
Spectral lines: 1λ=R(1n12−1n22) \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) λ1=R(n12 1 −n22 1 ), Rydberg constant R=1.097×107 R = 1.097 \times 10^7 R=1.097×107 m^{-1}.
Schrödinger's solution gives quantum numbers: principal n n n, orbital l=0ton−1 l = 0 to n-1 l=0ton−1, magnetic ml=−ltol m_l = -l to l ml=−ltol, spin ms=±12 m_s = \pm \frac{1}{2} ms=±21.
Pauli exclusion principle: No two electrons same quantum numbers.
