Describing Kinetic Energy(KE) Classically: Quantum Mechanically: -ihaΨ KE-1mv2 Px= 2πdx 2 Iffx,y,z）=x2+y3+z4, p=mv,so KE= p2 2m then a证=2xand 0 ay 3y2 Combining Equations: KEx p_82y-h2 (close enough for now!) 2m 0x2 8mn2 ,2如 KE-KEx+KEy+KEz-8m2 x2+y2 0z2 g产2 )(V is a form of mathematical shorthand notation -5∂f ∂ x ∂ f ∂ y — If f(x,y,z) = x2+y3+z4 , Describing Kinetic Energy (KE) Classically: Quantum Mechanically: then = 2x and = 3y2 px = −ih 2π ∂Ψ KE = ∂x 1 2 mv 2 p = mv , so KE = p 2 2 m Combining Equations: (close enough for now!) = - h 2 8 m π 2 ∇ 2 ( Ψ ) ( ∇ is a form of mathematical shorthand notation ) KE x = p x 2 2 m = ∂ 2 Ψ ∂ x 2 -h 2 8 m π 2 So KE =KE x + KE y +KE z = -h 2 8 m π 2 ∂ 2 Ψ ∂ x 2 + ∂ 2 Ψ ∂ y 2 + ∂ 2 Ψ ∂ z 2         III-5