The latter may be obtained from the previous free-particle result upon making use of van Kortryk's SU(1,1) Lie-group identity, exp ⁡ ⁡ ( − − i t ℏ ℏ ( 1 2 m p 2 + 1 2 m ω ω 2 x 2 ) ) = exp ⁡ ⁡ ( − − i m ω ω 2 ℏ ℏ x 2 tan ⁡ ⁡ ω ω t 2 ) exp ⁡ ⁡ ( − − i 2 m ω ω ℏ ℏ p 2 sin ⁡ ⁡ ( ω ω t ) ) exp ⁡ ⁡ ( − − i m ω ω 2 ℏ ℏ x 2 tan ⁡ ⁡ ω ω t 2 ) , valid for operators x and p satisfying the Heisenberg relation [ x , p ] = i ℏ ℏ .