WavePacket Wiki

Although the bound state energies and wavefunctions are known from Morse's original work, we use the example of the Morse oscillator to illustrate the performance of the numerical TISE solvers as implemented in WavePacket.

Direct diagonalization

The results obtained with the Fourier Grid Hamiltonian (FGH) method as implemented in WavePacket are in very good agreement with the analytically known eigenenergies. Even for the very highest, strongly anharmonic states we have at least four digits accuracy for a spatial grid with 256 points between r=0 and r=8 a₀, while the agreement is even much better for the lower states. For an analytical representation of Morse oscillator eigenstates in position, momentum, and phase space, see the work by J. P. Dahl and M. Springborg.

• Animated sequence of bound state wavefunctions
• Input data file
• Logfile output

Relaxation method

For comparison, we also show results of wavefunction relaxation, i.e., imaginary time propagation here. Even though numerically inferior, especially for higher excited states, that method is more suitable for higher dimensionality.