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hbar

Represents the reduced Planck constant, a fundamental physical constant used extensively in quantum mechanics.

Overview

Essential in quantum physics and related fields, appearing in equations describing wave functions, uncertainty relations, and quantum states.

  • Defined as Planck's constant divided by 2π
  • Frequently appears in Schrödinger's equation and quantum field theory
  • Common in academic papers and textbooks discussing quantum phenomena
  • Often used alongside other quantum mechanical operators and wave functions

Examples

Writing the time-independent Schrödinger equation in quantum mechanics.

Hψ=−ℏ22m∇2ψ+Vψ=EψH\psi = -\frac{\hbar^2}{2m}\nabla^2\psi + V\psi = E\psi 
H\psi = -\frac{\hbar^2}{2m}\nabla^2\psi + V\psi = E\psi

Expressing the uncertainty principle for position and momentum.

ΔxΔp≥ℏ2\Delta x \Delta p \geq \frac{\hbar}{2} 
\Delta x \Delta p \geq \frac{\hbar}{2}

Defining angular momentum quantization in quantum mechanics.

L=nℏL = n\hbar 
L = n\hbar