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 A while back you posted pics of your single leg plant vs other jumpers, I told you that you had a very knee dominant plant, this is the reason I think youre convinced your quads are the limiting factor in your jump, youre forcing more work on them than you need to.  The single leg wall sit is not a natural movment for the body, the hips are pinned and the torso is forced in a vertical position, a single leg squat iso to the same depth with a hand holding onto something beside you for balance is a better option imo.  The single leg standing glute bridge is a better option than both of them, you can focus on turning on the glute maximally in extension, strengthening the lower leg and getting as high on the big toe as possible, and stretches and strengthens the hip flexors simultaneously.  Working up to one minute while firing the glute, gastroc, and hip flexor maximally, the same way you will in a single leg jump, is a good starting place.  If you cant feel the glute firing on the iso, you damn sure arent going to be able to get to the glute in your jumps either.  Once you hit one minute on the iso you can easily hold dumbells by your sides.  In your case I think using something like this for a strength and activation movement would help you alot more and help you get to the glutes and posterior chain more in your jumps.

<a href="http://www.youtube.com/watch?v=eAaBXq90AAM" target="_blank">http://www.youtube.com/watch?v=eAaBXq90AAM</a> 
http://www.youtube.com/watch?v=eAaBXq90AAM

 
 Exactly, the more hip dominant you make your plant, the less that quad is going to be a factor.

  Yes, that one leg wall sit will strengthen the quads to a certain degree but I wouldnt do it if I were you, youre going to be amplifying an already existing problem. Youre essentially putting the glutes at a disadvantaged position and forcing the load on the knee.  You could get really good at them and amplify your already knee dominant plant or you could teach your body to "get to the glute/hips" and have the quads not be as big of a factor as they currently are.  People who squat with the hips pushed in and knees coming a mile forward think the quads are the limiting factor in their squat too, they are, they can either strengthen them even more or change the way they squat.

 Ive worked with alot of excellent single leg jumpers throughout my career, the ONE thing ALL of the great ones had in common was insane hamstring strength (as a hip extensor), and great glute and posterior chain dominance in their movments.  Even the skinny ones had unbelievable strength and power in the posterior chain, the quad strength varied between different jumpers but it was never anything ridiculous compared to other athletes.  Even in bilateral landings, etc., things you would expect to be more quad dominant, they would load the posterior chain with very little coaching. 

  Raptor,  just saw this, have to go train ppl but i will respond at lunch break. pc.

  The difference in quad strength you described is fitting , youre training the quads of your left leg extremely hard with all the unilateral quad dominant jumping.  The difference in the jumping right vs left can very well be a neural issue too, you likely dont practice jumping off of the right as much and even if you did, the posterior region of the right leg may not be as powerful as the quads have grown to be in your left leg in the jumping movement.  Alot of times when athletes learn to plant and jump differently, using the glutes and hams more off of one leg there will be an initial decrease in jumping height, the potential of the jump is much higher once this movement pattern is trained and solidified.  Another issue with typical strength exercises like squats, lunges, etc., is many people "overarch", they have an extreme curve in the low back, they are putting the hamstrings in a position to do more work than the glutes.  Both should be turned on but the glutes need to be loaded maximally in the single leg jump while the hamstrings assist the movement.

 Im very big on the standing glute iso hold shown, you can feel which muscle group is more active and many times it will be the hamstrings, you have to play with the pelvic position and learn to activate the lower abdominal region to really get to the glutes more.

 I like what youre currently doing in your program, once the low bar full squatting more than once per week levels off and youre not able to progress it linearly I would transition into one day per week of that squat and one day per week of a more spp movement like a single leg box squat, walking the working leg out a little in front of the body and working on getting the hips more active as well as speed-strength in the movement.  You can then progress both of them linearly for a long time, getting the best of both worlds.  

As far as the two legged jump and what youre telling andrew, its a different animal than the single leg jump by a long shot, if you were to relate the two to an upper body movement, think of the two leg jump as throwing a shot put with both hands like a bench press throw, and the single leg jump as throwing it like a baseball.  The role of the shoulder joint and chest (hips) is going to be different, and the role of the triceps (quads) is going to be even more different.  Different athletes with different structures, levers, strengths and weaknesses, etc, are going to use different muscles to different degrees in the two legged jumps just like they do in the bench press, some use much more tricep, some much more chest, etc.  

  Thats very common to get more upper hamstring/glute tie in on the iso at first, it seems almost counter intuitive but you need to learn to push down into the glute with abdominals, while maintaining neutral with the spine, this usually fixes it once youve gotten to the point of feeling more upper ham (beginners usually fail at the quads before they even get to the hams, intermediates and some pretty decent athletes can usually get to the upper hams/tie ins, excellent athletes and elite jumpers usually get to the glutes without much cueing i.m.e.) The better you get at firing the glutes maximally, staying as high as you can on the big toe (try to lift the pinky side of the foot up if need be), the more powerful and used to this position the body will be, you will notice the body "wants" to get to full hip extension in your jumps, lifts, sprints, etc.  You will also notice how much stronger you are in that position once the glutes are dominating the movement.  

  What you were saying about your body naturally changing the jumping movement once you performed it more and more, this is also something very true.  Strength training can negatively influence this if the movement patterns in the weight room are favoring a more dominant pattern (making lowerbody movements quad dominant like squats, lunges, etc.) for an athlete needing a hip dominant movement in athletics.  The body will respond to the strength training (squatting like you were a while back, knees coming way forward, not sitting back into the hips,etc.) and gain strength in that movement pattern very quickly, affecting your jumping movement as well.  IMO, this is what causes the common issue of single leg jumpers who started strength training becoming double leg jumpers, no longer jumping well off one leg, they were training the body in a manner more fitting for a double leg jump.  Had they gone about this differently, choosing different movements, learning a hip dominant squat, etc., this would not have been the issue, they would improve both single leg and double leg jumps, but not LOSE their ability to jump well off one leg.  In that particular case, the single leg jumping athlete would have been better off not re training the movement pattern in the weight room, in favor of the more quad dominant movment pattern they attained from the exercises they used (usually a quad dominant squat,or other quad dominant exercises), if single leg jumping were their main goal.

  I like the single leg box squat much more than the other options, reverse lunges would be next on the list but you have the ability to walk the working leg out in front of the body more and more, allowing more of a "pull" and hip extension in the manner used in your event youre trying to improve.  I have never gotten anywhere close to the carryover with other single leg exercises as i have with the single leg box squat, coupled with the single leg cleans.  The hip dominant jump needed to be proficient in the single leg clean carries over very nicely to jump with the added benefit of the landing, youre killing alot of birds with one stone this way.  If youre having trouble getting your hips into your cleans and snatches, start with knees almost locked, push the shoulders as far out over the bar as possible.  The double knee bend will be forced to happen this way and you will get a ton more hip involvement in the lift.  Using the iso hold as an activation movement before the cleans and snatches will help also, the body will "want" to use the glutes more automatically.

  Yea, you see lots of high jumpers doing half squats which is fine, you can learn to recruit the glutes and hams in a half squat very well.  If the goal was primarily two leg jumping, I would use half squats ALOT, as an spp type squat as well.  The low bar position saves the knees of my jumpers, ESPECIALLY triple jumpers.  When they come in they have usually stalled or gone backwards in their jumps, have at least some degree of knee pain/issues, and have been using typical high jump/long jump strength training protocals for several years.  The long leg/short torso build that is the majority in this case, take alot of stress off the knees with the lowered bar position, and get much more hamstring activity with it as well, even with a fair degree of knee travel (note that im referring to shoulder width, bar across upper rear delts, knees tracking over feet, stance).

  Yes, if the strength training is NEW to the athlete, and the athlete is not a competitive jumper, or jumping extremely frequently, then the new stimulus of the strength training is going to weigh very heavily on their on court/field/track performance.  This is not nearly the same thing as an olympic high jumper, jumping and doing jumping drills/practice, five days a week, and doing 4 sets of 5 high bar half squats twice a week.  

The range of motion.... what has worked the best is starting at a larger range of motion, using the eccentric on one leg as well, and building a "base" first.  As the season nears the box height increases to a rom more specific to the jump, then transitioning into bands as well as free weight, with a two leg eccentric, explosive single leg concentric on one leg.  I can do them this way up to two days before the track meet and get pr;s in jumps.  The parallel depth wouldnt be bad at first, you will develop some great single leg strength that way and thats pretty close to the offseason box height I use.  I want them to be able to walk the leg out in front a decent ways, but also get a larger rom than they jump out of.  

 

Youre exactly right, I like the bar on shoulders since it loads the posterior region much more than the pistol version, you can move the working leg out in front of the body, and you can get very strong at this exercise, the weights held in hand would cause you to fail at the shoulders or hands before you adequately challenged the jumping musculature.  Putting the leg straight out in front of the body as in a pistol squat changes the dynamics of what im after as well, the non working leg will slightly trail the working leg in the slbs, finishing in front with the knee. (I have stacked plates under benches, etc. in commercial gym settings before with this exercise so thats one way around not having a box).

Yea, film the cleans, from the hang.  Earlier I may have not done a very thorough job explaining what I meant when I was explaining how to get more hip into the olympic lifts, start by standing straight up, legs almost locked, descend into an rdl position, again, knees should be almost locked.  Bar should be about mid thigh, shoulders as far in front of the bar as possible, then simply JUMP.  What will happen is the knees will bend when the bar slides up higher on the thigh, but the hips rather than the quads are leading the lift.   You sound like youre starting behind the bar, with knees already bent at the beginning of the hang position, this should fix that issue.  

  I like the peterson step ups alot more, I dont think leg extensions are awful, I just dont use them with athletes.  One cue you dont see talked about often with step ups is to "pull" with the hams and glutes before you "push".  It will aid the knee stability, get the glute involved more, and transfer more weight onto the working leg.

 I worked with a bodybuilder a few years back that had problems with his vmo's, he had tried everything under the sun and they just wouldnt catch up with the rest of his leg development.  What worked was doing partials, at the bottom of the squat, he would go into a full squat, and "bounce" for 3 reps up to parallel and back down, then to a full standing position.  It was interesting as I tried different numbers with the partials at the bottom, 3 ended up being the most successful since the breath and tightness could be held for 3's, then he would return to a standing position after the 3rd and exhale, get another breath, and repeat.  In a typical set of 10 reps you get 30 reps at the bottom half this way, the vmo's responded insanely well with an added benefit of more glute development.   

  Just make really sure to include plenty of quad flexibility work as well, letting them tighten up on you is a good way to limit performance and have some more knee issues re appear.