Schrödinger’s equation: -(ħ²/2M)grad²φ(x,y,z) + Vφ(x,y,z) = Eφ( z,y,z) For a particle in a box: V = 0 if 0 < x,y,x < a = ∞ otherwise Try a solution of the form φ = Nsin(2πlx/a)sin(2πmy/a)sin(2πnz/a) Where N is the normalisation factor. φ must go to zero at x,y,z = a, therefore l,m,n are integers. So, E = -(1/2M)(2πħ/a)²(l² + m² + n²) Now, pressure P = ∂E/∂V And dV = d³a = d(a³) = 3a²da Therefore P = (1/3a²)∂E/∂a This is quantum pressure.