Simulation of the Schrödinger equation and atomic orbitals

The code for this project is based on this and this tutorial. As the tutorials did not provide all of the code necessary to replicate all the outputs, this repository offers a completed, slightly refined version.

Results

1D

Example 1: Gaussian wave packet with zero momentum

1d_sim1_color.mp4

1d_sim1_re_im.mp4

---

Example 2: Gaussian wave packet with nonzero momentum

1d_sim2_color.mp4

1d_sim2_re_im.mp4

---

Example 3: Particle in a box

1d_sim3_color.mp4

1d_sim3_re_im.mp4

---

Example 4: Weak barrier aka quantum tunneling

1d_sim4_color.mp4

1d_sim4_re_im.mp4

---

Example 5: Quadratic potential aka quantum harmonic oscillator

1d_sim5_color.mp4

1d_sim5_re_im.mp4

---

Example 6: Finding groundstate aka lowest energy eigenstate

1d_sim6_color.mp4

1d_sim6_re_im.mp4

---

Example 7: Finding excited state

1d_sim7_re_im.mp4

---

Example 8: Time evolution of found excited state

1d_sim8_color.mp4

1d_sim8_re_im.mp4

---

2D

Example 1: Gaussian wave packet with zero momentum

2d_sim1.mp4

---

Example 2: Gaussian wave packet with nonzero momentum, only momentum in x-direction

2d_sim2.mp4

---

Example 3: Gaussian wave packet with nonzero momentum, momentum in x- and y-direction

2d_sim3.mp4

---

Example 4: Particle in a box

2d_sim4.mp4

---

Example 5: Weak barrier aka quantum tunneling

2d_sim5.mp4

---

Example 6: Radial quadratic potential

2d_sim6.mp4

---

Example 7: Orbitals in 2D

---

1S Orbital

2d_sim7_1s.mp4

---

2P Orbital

2d_sim7_2p.mp4

---

2S Orbital (using generic guess)

2d_sim7_2s_generic_guess.mp4

---

1S Orbital (using boring/too good guess)

2d_sim7_2s_specific_guess.mp4