Short answer: Yes — but with caveats. A square/coax-to-waveguide adapter can act as a waveguide feed/aperture for a 1.5 m dish at the hydrogen line, provided its internal dimensions support the dominant waveguide mode at 1420.405 MHz and you take care of matching, mode excitation, and illumination. If you treat the adapter as a simple radiating aperture without those checks you’ll very likely get poor efficiency, high spillover and a bad match.

Below are the important points, calculations, and practical steps.

Quick numbers (for 1420.405 MHz)

• Free-space wavelength λ = c / f ≈ 0.211 m (211 mm).
• Your 1.5 m dish is ~7.11 λ across (1.5 / 0.211).
• With a reasonable aperture efficiency (≈0.55) the dish gain ≈ 24.4 dBi (useful to know when estimating system temperature / SNR).

Waveguide size / cutoff

• For a rectangular/square waveguide the cutoff for the dominant TE₁₀ mode is approximately fc = c / (2a) where a is the larger side.
• To support 1420 MHz you need fc < 1420 MHz → a > c/(2·1420e6) ≈ 105.5 mm (i.e. side > ~105 mm).
  • Example: WR-650 (a ≈165 mm) has fc well below 1420 MHz and will support TE₁₀ comfortably; a smaller waveguide with side <105 mm will not support the mode (or will be near cutoff, with high loss/dispersion).

What can go wrong if you just stick an adapter on the feed

• Mode / pattern mismatch: Lab adapters are designed to transition coax to waveguide modes for measurement, not to produce the smooth, tapered illumination a dish needs. The aperture field distribution may be uneven (giving sidelobes and low aperture efficiency).
• Impedance / return loss: Without a proper probe depth/backshort or matching structure, S11 can be poor.
• Polarization & mechanical alignment: Adapter may not present the required polarization or phase center position for correct focal illumination.
• Spillover & noise: If the aperture is too small or poorly shaped, power will spill past the dish and increase system noise (especially important for faint hydrogen signals).
• Bandwidth / resonances: A short adapter might produce resonances or narrowband behavior unless properly designed.

When it will work reasonably well

• The adapter/waveguide inner dimension is large enough (see cutoff above).
• You can excite the correct dominant mode (proper probe placement / backshort).
• The aperture size and pattern give a reasonable edge taper on the dish (typically −10 to −13 dB edge taper is a good target).
• You can measure and tune the match (S11) and the radiation pattern or at least check illumination with measurements.

Practical recommendations / checklist

1. Check internal dimension of the adapter. If side ≥ ~110 mm you’re in the safe zone for TE₁₀ at 1420 MHz.
2. Use a proper waveguide→coax transition (probe + backshort) rather than just a connector stub. Probe depth and backshort distance are critical to excite the TE₁₀ cleanly and get a good match.
3. Measure return loss with a VNA (or loan one / use a test rig). Aim for S11 < −10 to −15 dB across your IF/band of interest.
4. Check the radiation pattern / edge taper. If you can’t measure pattern, at least measure on-sky system temperature and compare against expectations (cold sky vs ambient load) to estimate efficiency.
5. Adjust position so the phase center of the adapter/feed sits at the dish focal point. Small axial shifts can change illumination a lot.
6. Consider a small matching/horn throat. Putting a short pyramidal or conical horn on the waveguide aperture smooths the pattern and improves illumination and matching. A simple pyramidal horn is often a cheap, high-gain improvement.
7. Control polarization. Ensure the adapter orientation matches the intended polarization (linear, RHCP/LHCP if required).
8. Mechanical mounting & weatherproofing. Make a sturdy mount so the aperture is stable at the focal point, and seal against moisture.

Alternatives (often easier / better)

• A small pyramidal or conical horn sized for 1420 MHz — gives predictable pattern and good illumination.
• A λ/2 dipole + balun positioned at the focus (cheap and commonly used on small radio astronomy dishes).
• A short circular waveguide feeding a small conical/horn throat (very efficient and commonly used in hydrogen-line feeds).

How to test if your adapter-feed is acceptable

• Measure S11 vs frequency with a VNA. Tune probe/backshort until match is acceptable.
• Point at the Sun (or strong radio source) and do an on/off measurement: compare measured antenna temperature to theoretical expectation for dish gain — gives a quick idea of aperture efficiency.
• If you have a calibration noise source or hot/cold load you can measure system temperature and estimate aperture efficiency quantitatively.

Bottom line

You can use a square coaxial→waveguide adapter as a feed on a 1.5 m hydrogen-line dish if the adapter dimensions support TE₁₀ at 1420 MHz and you take pains to excite the correct mode, match the impedance, and achieve a sensible illumination/edge taper. For best results consider adding a short horn or proper transition rather than relying on the bare adapter as the radiator.