What you're asking is if a neutron star has a habitable zone. The answer is NO. Either all plants die from lack of sunlight, or it's too hot, or you're sterilized by X-rays.
To be habitable you need an orbit where there's enough light for photosynthesis to work, the right temperature for liquid water, and not too much high-energy light (X-rays, gamma rays) to overwhelm being absorbed by the atmosphere (which makes things even hotter).
As far as liquid water is concerned you can probably find one for a neutron star, they're typically about 1 to 2 times the mass of the Sun and put out about $\frac{1}{3}$ the energy, so it would have to be closer than the Earth is to our Sun, but not so close we need to worry about being torn apart by tidal forces at about 700,000 km.
I'm not going to go into that further because there's a bigger problem: the type of radiation.
A typical neutron star has a surface temperature of $6\cdot 10^{5}~\text{K}$ (100 times hotter than the Sun). From this we can determine what type of radiation will be most powerful using Wien's displacement law for blackbody radiation.
$\text{max wavelength} = \frac{\text{Wien's displacement constant}}{\text{surface temperature}}$
As you can see, wavelength will drop as the surface temperature gets higher. Since the Sun puts out lots of visible light, and a neutron star is 100 times hotter, this isn't going to go well for our new Earth. When we plug in the numbers...
$\text{max wavelength} = \frac{2.90\cdot 10^{−3}~\text{K m}}{6\cdot 10^{5}~\text{K}} = 4.833\cdot 10^{-9}~\text{m}$
About 5 nanometers which puts us firmly into X-rays. This is bad for life.
While Earth's atmosphere absorbs most everything with more energy than visible light the Sun doesn't put out a lot of X-Rays in the first place.

Note that graph is exponential, our Sun is putting out a million times more visible light than X-rays, our atmosphere can handle that. Our neutron star slides that line to the left. The maximum output will be firmly in X-rays. It will be putting out a million times more X-rays than our Sun. It will also be putting out 1,000 times less visible light causing problems for photosynthesis.
Because a neutron star puts out about $\frac{1}{3}$ the energy of our Sun, we only need to be a little closer to get enough heat. But because there's 1,000 times less little visible light than the Sun, we need to be much, much closer for photosynthesis to work. But that close we'll be fried by heat. Getting closer to get 1,000 times more visible light also gives us 1,000 times more X-rays which puts us at a billion times the X-rays from our Sun! Our atmosphere cannot protect us from that, or if it could the absorbed energy transferred to heat would fry us even further.
An atmosphere engineered to deal with this would need to reflect (not absorb) most of the energy coming from the neutron star, while still letting through nearly all of the visible light, and still be friendly to life as we know it. I don't think such an atmosphere is possible.
Alternatively, riffing on this answer, the atmosphere would need to convert X-ray radiation into visible light while still being acceptable to life. This reaction, if balanced correctly, would allow the planet to generate enough visible light for plants and heat for liquid water while protecting the surface from X-rays. I don't know of any substance which could do this, but I'm not a chemist.
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