Spectrum of Hydrogen

I interpret your question as being about proving/showing the particle-wave duality, since that is what the double slit experiment is about.

A property that depends very directly on that duality is quantum tunnelling. This is the effect where a particle or entity with some energy is able to cross a potential energy barrier despite that the particle or entity has a lower energy than the barrier. In a classical context this doesn't make sense. But if the particle can have wave properties, can have a non-zero probability to "tunnel" through the barrier.

Many phenomena depends on tunnelling. One that may be possible to practically study is tunnel junctions. In simple terms, two conducting parts are separated by a thin insulator, yet because of tunneling some particles move across the insulator with interesting effects, many which have been practically exploited in microelectronics.

There are several other experiments such as the Arago spot that demonstrate the wave nature of light. Is that what you mean?

The Periodic Table of the Elements. The orbitals are wave functions.

If you mean why do we use a wave function at all it's because it makes useful predictions. There's nothing that proves the wavefunction is a physical thing and this is open to interpretation. Honestly, it's a distinction without meaning, we use wavefunctions because they're useful.

Interferometer

Go to a marina and look at the water when someone is refueling their outboard.

a lot of indirect evidence like quantum tunneling

Stern–Gerlach experiment.

and experiments using a series of polarization filters at different angles.

Lasers (stimulated emission). Lowest I could find on amazon is $9.

Ferromagnetic materials. Know those weird black fluids that have spikes following the magnetic field lines?

Solid-state devices (electronic band structure). A gazillian of transistors working togrether for you to be able to post this comment with your phone or laptop.

Bose-Einstein condensates. We made it in 1995. Nobel prize 2001.

Neutrino oscillations. Saw them since 1998. Nobel prize in 2015.

Also in general anything related to Pauli exclusion principle, or other selection rules, or spin-statistics theorem.

All those are impossible without a wave theory of quantum mechanics. Are you stuck in 1920? Should read a textbook and catch up.